EDP Sciences 1776416902 20260417 fre

laboutique.edpsciences.fr-R001919 03 01 01 R001919 00 ED E107 00 01 01 Solutions to Linear Matrix Equations and Their Applications 01 eng 08 198 03 22 2957962 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 11 00 20230720 02 01 002301 03 9782759831036 15 9782759831036 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-002301 03 01 01 002301 03 9782759831036 15 9782759831036 10 EA E107 10 00 01 R001919 ED E107 1 10 01 02 Current Natural Sciences 01 01 Solutions to Linear Matrix Equations and Their Applications 1 A01 01 A2164 Caiqin SONG SONG, Caiqin Caiqin SONG Caiqin SONG is an associate professor at University of Jinan. She received her PhD from East China Normal University in 2012. Her research focuses on the explicit method of linear matrix equations, the iterative algorithm of linear matrix equations, the explicit method of quaternion matrix equations, and problems on the semi-tensor product of matrix, etc. She is the author of more than 30 publications in international academic journals and has chaired national and provincial commissions of research funding programs. 01 eng 08 196 03 01 20 algorithm;CGLS;linear;equations;Sylvester-conjugate;professionals;Sylvester-conjugate;finite iterative algorithm;generalized Sylvester matrix equation 10 2011 MAT019000 01 510 06 06 05 03 00 This book addresses both the basic and applied aspects of the finite iterative algorithm, CGLS iterative algorithm, and explicit algorithm to some linear matrix equations. The author presents the latest results in three parts: (1) We consider the finite iterative algorithm to the coupled transpose matrix equations and the coupled operator matrix equations with sub-matrix constrained. These two finite iterative algorithms are closely related and progressive. (2) We present MCGLS iterative algorithm for studying least squares problems to the generalized Sylvester-conjugate matrix equation, the generalized Sylvester-conjugate transpose matrix equation, and the coupled linear operator systems, respectively. (3) Compared with the previous two parts, we consider here the explicit solution to some linear matrix equations, which are the nonhomogeneous Yakubovich matrix equation, the nonhomogeneous Yakubovich transpose matrix equation, and the generalized Sylvester matrix equation, respectively. This book is intended for students, researchers, and professionals in the field of numerical algebra, linear matrix equations, nonlinear matrix equations, and control theory. 02 00 This book addresses both the basic and applied aspects of the finite iterative algorithm, CGLS iterative algorithm, and explicit algorithm to some linear matrix equations 04 00 About the Author ............................................ III<o:p></o:p>Preface..................................................... V<o:p></o:p>Notations................................................... VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 The First Part: Finite Iterative Algorithm to Linear Matrix Equation . 1<o:p></o:p>1.2 The Second Part: MCGLS Iterative Algorithm to Linear Matrix Equation............................................... 31.3 The Third Part: Explicit Solutions to Linear Matrix Equation ...... 5<o:p></o:p>CHAPTER 2<o:p></o:p>Finite Iterative Algorithm to Coupled Transpose Matrix Equations ....... 11<o:p></o:p>2.1 Finite Iterative Algorithm and Convergence Analysis ............. 12<o:p></o:p>2.2 Numerical Example ....................................... 24<o:p></o:p>2.3 Control Application ...................................... 27<o:p></o:p>2.4 Conclusions............................................. 28<o:p></o:p>CHAPTER 3<o:p></o:p>Finite Iterative Algorithm to Coupled Operator Matrix Equations withSub-Matrix Constrained .................................... 293.1Iterative Method for Solving Problem 3.1 ...................... 30<o:p></o:p>3.2Iterative Method for Solving Problem 3.2 ...................... 41<o:p></o:p>3.3 Numerical Example ....................................... 42<o:p></o:p>3.4 Control Application ...................................... 53<o:p></o:p>3.5 Conclusions............................................. 54<o:p></o:p>CHAPTER 4<o:p></o:p>MCGLSIterative Algorithm to Linear Conjugate Matrix Equation ........ 55<o:p></o:p>4.1 MCGL SIterative Algorithm and Convergence Analysis............ 57<o:p></o:p>4.2 Numerical Example ....................................... 66<o:p></o:p>4.3 ControlApplication ...................................... 73<o:p></o:p>4.4 Conclusions............................................. 74<o:p></o:p>CHAPTER 5<o:p></o:p>MCGLS Iterative Algorithm to Linear Conjugate Transpose Matrix Equation................................................... 755.1 MCGLS Iterative Algorithm and Convergence Analysis............ 78<o:p></o:p>5.2 Numerical Example ....................................... 90<o:p></o:p>5.3 Conclusions............................................. 95<o:p></o:p>CHAPTER 6<o:p></o:p>MCGLS Iterative Algorithm to Coupled Linear Operator Systems ........ 97<o:p></o:p>6.1 Some Useful Lemmas ..................................... 98<o:p></o:p>6.2 MCGLS Iterative Algorithm and Convergence Analysis............ 99<o:p></o:p>6.3 Numerical Examples ...................................... 107<o:p></o:p>6.4 Conclusions............................................. 113<o:p></o:p>CHAPTER 7<o:p></o:p>Explicit Solutions to the Matrix Equation X − AXB = CY + R .......... 115<o:p></o:p>7.1 Solutions to the Real Matrix Equation X − AXB = CY + R ....... 115<o:p></o:p>7.2 Parametric Pole Assignment for Descriptor Linear Systems by P-DFeedback ........................................ 1247.3 Conclusions............................................. 128<o:p></o:p>CHAPTER 8<o:p></o:p>Explicit Solutions to the Non homogeneous Yakubovich-Transpose Matrix Equation................................................... 1318.1 The First Approach ...................................... 132<o:p></o:p>8.2 The Second Approach ..................................... 140<o:p></o:p>8.3 Illustrative Example ...................................... 142<o:p></o:p>8.4 Conclusions............................................. 143<o:p></o:p>CHAPTER 9<o:p></o:p>Explicit Solutions to the Matrix Equations XB-AX = CY.......................................... 145<o:p></o:p>9.1 Real Matrix Equation XB − AX = CY and XB - AX = CY  ........................ 1459.2 Quaternion-j-Conjugate Matrix Equation XB − AX = CY......... 148<o:p></o:p>9.2.1 Real Representation of a Quaternion Matrix .............. 148<o:p></o:p>9.2.2 Solutions to the Quaternion j-Conjugate Matrix Equation XB − AX =CY ................................... 1509.3 Conclusions............................................. 155<o:p></o:p>CHAPTER 10 Explicit Solutions to Linear Transpose Matrix Equation ................ 157<o:p></o:p>10.1Solutions to the Sylvester Transpose Matrix Equation ............ 157<o:p></o:p>10.1.1 The First Case: A or B is Nonsingular ................. 158<o:p></o:p>10.1.2 The Second Case: A and B are Nonsingular ............. 162<o:p></o:p>10.2 Solutions to the Generalized Sylvester Transpose Matrix Equation . . 165<o:p></o:p>10.3 Algorithms for Solving Two Transpose Equations and Numerical Example.............................................. 16810.4 Application in Control Theory ............................. 174<o:p></o:p>10.5 Conclusions ............................................ 175<o:p></o:p>References.................................................. 177<o:p></o:p> About theAuthor ............................................ III<o:p></o:p>Preface..................................................... V<o:p></o:p>Notations................................................... VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 TheFirst Part: Finite Iterative Algorithm to Linear Matrix Equation . 1<o:p></o:p>1.2 TheSecond Part: MCGLS Iterative Algorithm to Linear Matrix<o:p></o:p>Equation............................................... 3<o:p></o:p>1.3 TheThird Part: Explicit Solutions to Linear Matrix Equation ...... 5<o:p></o:p>CHAPTER 2<o:p></o:p>FiniteIterative Algorithm to Coupled Transpose Matrix Equations ....... 11<o:p></o:p>2.1 FiniteIterative Algorithm and Convergence Analysis ............. 12<o:p></o:p>2.2Numerical Example ....................................... 24<o:p></o:p>2.3 ControlApplication ...................................... 27<o:p></o:p>2.4Conclusions............................................. 28<o:p></o:p>CHAPTER 3<o:p></o:p>FiniteIterative Algorithm to Coupled Operator Matrix Equations<o:p></o:p>withSub-Matrix Constrained .................................... 29<o:p></o:p>3.1Iterative Method for Solving Problem 3.1 ...................... 30<o:p></o:p>3.2Iterative Method for Solving Problem 3.2 ...................... 41<o:p></o:p>3.3Numerical Example ....................................... 42<o:p></o:p>3.4 ControlApplication ...................................... 53<o:p></o:p>3.5Conclusions............................................. 54<o:p></o:p>CHAPTER 4<o:p></o:p>MCGLSIterative Algorithm to Linear Conjugate Matrix Equation ........ 55<o:p></o:p>4.1 MCGLSIterative Algorithm and Convergence Analysis............ 57<o:p></o:p>4.2Numerical Example ....................................... 66<o:p></o:p>4.3 ControlApplication ...................................... 73<o:p></o:p>4.4Conclusions............................................. 74<o:p></o:p>CHAPTER 5<o:p></o:p>MCGLSIterative Algorithm to Linear Conjugate Transpose Matrix<o:p></o:p>Equation................................................... 75<o:p></o:p>5.1 MCGLSIterative Algorithm and Convergence Analysis............ 78<o:p></o:p>5.2Numerical Example ....................................... 90<o:p></o:p>5.3Conclusions............................................. 95<o:p></o:p>CHAPTER 6<o:p></o:p>MCGLSIterative Algorithm to Coupled Linear Operator Systems ........ 97<o:p></o:p>6.1 SomeUseful Lemmas ..................................... 98<o:p></o:p>6.2 MCGLSIterative Algorithm and Convergence Analysis............ 99<o:p></o:p>6.3Numerical Examples ...................................... 107<o:p></o:p>6.4Conclusions............................................. 113<o:p></o:p>CHAPTER 7<o:p></o:p>ExplicitSolutions to the Matrix Equation X − AXB = CY + R .......... 115<o:p></o:p>7.1 Solutionsto the Real Matrix Equation X − AXB = CY + R ....... 115<o:p></o:p>7.2Parametric Pole Assignment for Descriptor Linear Systems<o:p></o:p>by P-DFeedback ........................................ 124<o:p></o:p>7.3Conclusions............................................. 128<o:p></o:p>CHAPTER 8<o:p></o:p>ExplicitSolutions to the Nonhomogeneous Yakubovich-Transpose Matrix<o:p></o:p>Equation................................................... 131<o:p></o:p>8.1 TheFirst Approach ...................................... 132<o:p></o:p>8.2 TheSecond Approach ..................................... 140<o:p></o:p>8.3Illustrative Example ...................................... 142<o:p></o:p>8.4Conclusions............................................. 143<o:p></o:p>CHAPTER 9<o:p></o:p>ExplicitSolutions to the Matrix Equations XB <hr align="left" size="1"><hr align="left" size="1"> AXb ¼ CY.......................................... 145<o:p></o:p>9.1 RealMatrix Equation XB − AX = CY ........................ 145<o:p></o:p>9.2 Quaternion-j-Conjugate Matrix Equation XB − AXb = CY......... 148<o:p></o:p>9.2.1 RealRepresentation of a Quaternion Matrix .............. 148<o:p></o:p>9.2.2Solutions to the Quaternion j-Conjugate Matrix Equation<o:p></o:p>XB − AXb =CY ................................... 150<o:p></o:p>9.3Conclusions............................................. 155<o:p></o:p>X Contents<o:p></o:p>CHAPTER 10<o:p></o:p>ExplicitSolutions to Linear Transpose Matrix Equation ................ 157<o:p></o:p>10.1Solutions to the Sylvester Transpose Matrix Equation ............ 157<o:p></o:p>10.1.1 TheFirst Case: A or B is Nonsingular ................. 158<o:p></o:p>10.1.2 TheSecond Case: A and B are Nonsingular ............. 162<o:p></o:p>10.2 Solutionsto the Generalized Sylvester Transpose Matrix Equation . . 165<o:p></o:p>10.3Algorithms for Solving Two Transpose Equations and Numerical<o:p></o:p>Example.............................................. 168<o:p></o:p>10.4Application in Control Theory ............................. 174<o:p></o:p>10.5Conclusions ............................................ 175<o:p></o:p>References.................................................. 177<o:p></o:p> 21 00 06 01 https://laboutique.edpsciences.fr/produit/1353/9782759831036/solutions-to-linear-matrix-equations-and-their-applications 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/982/971/original/9782759831029-Solutions_to_Linear_Matrix_Equations_and_their_Applications_couv-sofedis.jpg 17 14 20240913T181941+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20230720 01 00 20230720 19 00 20230720 2026 06 3052868830012 01 WORLD 13 03 9782759831029 15 9782759831029 06 03 9782759831043 15 9782759831043 WORLD 08 EDP Sciences & Science Press 04 01 00 20230720 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 65.99 01 5.50 3.44 EUR 04 06 01 02 1 00 231.99 01 5.50 3.44 EUR 01 04 06 01 02 1 00 255.99 01 5.50 13.35 USD 01 laboutique.edpsciences.fr-002669 03 01 01 002669 03 9782759831043 15 9782759831043 10 EA 10 10 01 02 Current Natural Sciences 01 01 Solutions to Linear Matrix Equations and Their Applications 1 A01 01 A2164 Caiqin SONG SONG, Caiqin Caiqin SONG Caiqin SONG is an associate professor at University of Jinan. She received her PhD from East China Normal University in 2012. Her research focuses on the explicit method of linear matrix equations, the iterative algorithm of linear matrix equations, the explicit method of quaternion matrix equations, and problems on the semi-tensor product of matrix, etc. She is the author of more than 30 publications in international academic journals and has chaired national and provincial commissions of research funding programs. 01 eng 08 196 03 01 20 algorithm;CGLS;linear;equations;Sylvester-conjugate;professionals;Sylvester-conjugate;finite iterative algorithm;generalized Sylvester matrix equation 10 2011 MAT019000 01 510 06 06 05 03 00 This book addresses both the basic and applied aspects of the finite iterative algorithm, CGLS iterative algorithm, and explicit algorithm to some linear matrix equations. The author presents the latest results in three parts: (1) We consider the finite iterative algorithm to the coupled transpose matrix equations and the coupled operator matrix equations with sub-matrix constrained. These two finite iterative algorithms are closely related and progressive. (2) We present MCGLS iterative algorithm for studying least squares problems to the generalized Sylvester-conjugate matrix equation, the generalized Sylvester-conjugate transpose matrix equation, and the coupled linear operator systems, respectively. (3) Compared with the previous two parts, we consider here the explicit solution to some linear matrix equations, which are the nonhomogeneous Yakubovich matrix equation, the nonhomogeneous Yakubovich transpose matrix equation, and the generalized Sylvester matrix equation, respectively. This book is intended for students, researchers, and professionals in the field of numerical algebra, linear matrix equations, nonlinear matrix equations, and control theory. 02 00 This book addresses both the basic and applied aspects of the finite iterative algorithm, CGLS iterative algorithm, and explicit algorithm to some linear matrix equations 04 00 About the Author ............................................ III<o:p></o:p>Preface..................................................... V<o:p></o:p>Notations................................................... VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 The First Part: Finite Iterative Algorithm to Linear Matrix Equation . 1<o:p></o:p>1.2 The Second Part: MCGLS Iterative Algorithm to Linear Matrix Equation............................................... 31.3 The Third Part: Explicit Solutions to Linear Matrix Equation ...... 5<o:p></o:p>CHAPTER 2<o:p></o:p>Finite Iterative Algorithm to Coupled Transpose Matrix Equations ....... 11<o:p></o:p>2.1 Finite Iterative Algorithm and Convergence Analysis ............. 12<o:p></o:p>2.2 Numerical Example ....................................... 24<o:p></o:p>2.3 Control Application ...................................... 27<o:p></o:p>2.4 Conclusions............................................. 28<o:p></o:p>CHAPTER 3<o:p></o:p>Finite Iterative Algorithm to Coupled Operator Matrix Equations withSub-Matrix Constrained .................................... 293.1Iterative Method for Solving Problem 3.1 ...................... 30<o:p></o:p>3.2Iterative Method for Solving Problem 3.2 ...................... 41<o:p></o:p>3.3 Numerical Example ....................................... 42<o:p></o:p>3.4 Control Application ...................................... 53<o:p></o:p>3.5 Conclusions............................................. 54<o:p></o:p>CHAPTER 4<o:p></o:p>MCGLSIterative Algorithm to Linear Conjugate Matrix Equation ........ 55<o:p></o:p>4.1 MCGL SIterative Algorithm and Convergence Analysis............ 57<o:p></o:p>4.2 Numerical Example ....................................... 66<o:p></o:p>4.3 ControlApplication ...................................... 73<o:p></o:p>4.4 Conclusions............................................. 74<o:p></o:p>CHAPTER 5<o:p></o:p>MCGLS Iterative Algorithm to Linear Conjugate Transpose Matrix Equation................................................... 755.1 MCGLS Iterative Algorithm and Convergence Analysis............ 78<o:p></o:p>5.2 Numerical Example ....................................... 90<o:p></o:p>5.3 Conclusions............................................. 95<o:p></o:p>CHAPTER 6<o:p></o:p>MCGLS Iterative Algorithm to Coupled Linear Operator Systems ........ 97<o:p></o:p>6.1 Some Useful Lemmas ..................................... 98<o:p></o:p>6.2 MCGLS Iterative Algorithm and Convergence Analysis............ 99<o:p></o:p>6.3 Numerical Examples ...................................... 107<o:p></o:p>6.4 Conclusions............................................. 113<o:p></o:p>CHAPTER 7<o:p></o:p>Explicit Solutions to the Matrix Equation X − AXB = CY + R .......... 115<o:p></o:p>7.1 Solutions to the Real Matrix Equation X − AXB = CY + R ....... 115<o:p></o:p>7.2 Parametric Pole Assignment for Descriptor Linear Systems by P-DFeedback ........................................ 1247.3 Conclusions............................................. 128<o:p></o:p>CHAPTER 8<o:p></o:p>Explicit Solutions to the Non homogeneous Yakubovich-Transpose Matrix Equation................................................... 1318.1 The First Approach ...................................... 132<o:p></o:p>8.2 The Second Approach ..................................... 140<o:p></o:p>8.3 Illustrative Example ...................................... 142<o:p></o:p>8.4 Conclusions............................................. 143<o:p></o:p>CHAPTER 9<o:p></o:p>Explicit Solutions to the Matrix Equations XB-AX = CY.......................................... 145<o:p></o:p>9.1 Real Matrix Equation XB − AX = CY and XB - AX = CY  ........................ 1459.2 Quaternion-j-Conjugate Matrix Equation XB − AX = CY......... 148<o:p></o:p>9.2.1 Real Representation of a Quaternion Matrix .............. 148<o:p></o:p>9.2.2 Solutions to the Quaternion j-Conjugate Matrix Equation XB − AX =CY ................................... 1509.3 Conclusions............................................. 155<o:p></o:p>CHAPTER 10 Explicit Solutions to Linear Transpose Matrix Equation ................ 157<o:p></o:p>10.1Solutions to the Sylvester Transpose Matrix Equation ............ 157<o:p></o:p>10.1.1 The First Case: A or B is Nonsingular ................. 158<o:p></o:p>10.1.2 The Second Case: A and B are Nonsingular ............. 162<o:p></o:p>10.2 Solutions to the Generalized Sylvester Transpose Matrix Equation . . 165<o:p></o:p>10.3 Algorithms for Solving Two Transpose Equations and Numerical Example.............................................. 16810.4 Application in Control Theory ............................. 174<o:p></o:p>10.5 Conclusions ............................................ 175<o:p></o:p>References.................................................. 177<o:p></o:p> About theAuthor ............................................ III<o:p></o:p>Preface..................................................... V<o:p></o:p>Notations................................................... VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 TheFirst Part: Finite Iterative Algorithm to Linear Matrix Equation . 1<o:p></o:p>1.2 TheSecond Part: MCGLS Iterative Algorithm to Linear Matrix<o:p></o:p>Equation............................................... 3<o:p></o:p>1.3 TheThird Part: Explicit Solutions to Linear Matrix Equation ...... 5<o:p></o:p>CHAPTER 2<o:p></o:p>FiniteIterative Algorithm to Coupled Transpose Matrix Equations ....... 11<o:p></o:p>2.1 FiniteIterative Algorithm and Convergence Analysis ............. 12<o:p></o:p>2.2Numerical Example ....................................... 24<o:p></o:p>2.3 ControlApplication ...................................... 27<o:p></o:p>2.4Conclusions............................................. 28<o:p></o:p>CHAPTER 3<o:p></o:p>FiniteIterative Algorithm to Coupled Operator Matrix Equations<o:p></o:p>withSub-Matrix Constrained .................................... 29<o:p></o:p>3.1Iterative Method for Solving Problem 3.1 ...................... 30<o:p></o:p>3.2Iterative Method for Solving Problem 3.2 ...................... 41<o:p></o:p>3.3Numerical Example ....................................... 42<o:p></o:p>3.4 ControlApplication ...................................... 53<o:p></o:p>3.5Conclusions............................................. 54<o:p></o:p>CHAPTER 4<o:p></o:p>MCGLSIterative Algorithm to Linear Conjugate Matrix Equation ........ 55<o:p></o:p>4.1 MCGLSIterative Algorithm and Convergence Analysis............ 57<o:p></o:p>4.2Numerical Example ....................................... 66<o:p></o:p>4.3 ControlApplication ...................................... 73<o:p></o:p>4.4Conclusions............................................. 74<o:p></o:p>CHAPTER 5<o:p></o:p>MCGLSIterative Algorithm to Linear Conjugate Transpose Matrix<o:p></o:p>Equation................................................... 75<o:p></o:p>5.1 MCGLSIterative Algorithm and Convergence Analysis............ 78<o:p></o:p>5.2Numerical Example ....................................... 90<o:p></o:p>5.3Conclusions............................................. 95<o:p></o:p>CHAPTER 6<o:p></o:p>MCGLSIterative Algorithm to Coupled Linear Operator Systems ........ 97<o:p></o:p>6.1 SomeUseful Lemmas ..................................... 98<o:p></o:p>6.2 MCGLSIterative Algorithm and Convergence Analysis............ 99<o:p></o:p>6.3Numerical Examples ...................................... 107<o:p></o:p>6.4Conclusions............................................. 113<o:p></o:p>CHAPTER 7<o:p></o:p>ExplicitSolutions to the Matrix Equation X − AXB = CY + R .......... 115<o:p></o:p>7.1 Solutionsto the Real Matrix Equation X − AXB = CY + R ....... 115<o:p></o:p>7.2Parametric Pole Assignment for Descriptor Linear Systems<o:p></o:p>by P-DFeedback ........................................ 124<o:p></o:p>7.3Conclusions............................................. 128<o:p></o:p>CHAPTER 8<o:p></o:p>ExplicitSolutions to the Nonhomogeneous Yakubovich-Transpose Matrix<o:p></o:p>Equation................................................... 131<o:p></o:p>8.1 TheFirst Approach ...................................... 132<o:p></o:p>8.2 TheSecond Approach ..................................... 140<o:p></o:p>8.3Illustrative Example ...................................... 142<o:p></o:p>8.4Conclusions............................................. 143<o:p></o:p>CHAPTER 9<o:p></o:p>ExplicitSolutions to the Matrix Equations XB <hr align="left" size="1"><hr align="left" size="1"> AXb ¼ CY.......................................... 145<o:p></o:p>9.1 RealMatrix Equation XB − AX = CY ........................ 145<o:p></o:p>9.2 Quaternion-j-Conjugate Matrix Equation XB − AXb = CY......... 148<o:p></o:p>9.2.1 RealRepresentation of a Quaternion Matrix .............. 148<o:p></o:p>9.2.2Solutions to the Quaternion j-Conjugate Matrix Equation<o:p></o:p>XB − AXb =CY ................................... 150<o:p></o:p>9.3Conclusions............................................. 155<o:p></o:p>X Contents<o:p></o:p>CHAPTER 10<o:p></o:p>ExplicitSolutions to Linear Transpose Matrix Equation ................ 157<o:p></o:p>10.1Solutions to the Sylvester Transpose Matrix Equation ............ 157<o:p></o:p>10.1.1 TheFirst Case: A or B is Nonsingular ................. 158<o:p></o:p>10.1.2 TheSecond Case: A and B are Nonsingular ............. 162<o:p></o:p>10.2 Solutionsto the Generalized Sylvester Transpose Matrix Equation . . 165<o:p></o:p>10.3Algorithms for Solving Two Transpose Equations and Numerical<o:p></o:p>Example.............................................. 168<o:p></o:p>10.4Application in Control Theory ............................. 174<o:p></o:p>10.5Conclusions ............................................ 175<o:p></o:p>References.................................................. 177<o:p></o:p> 21 00 06 01 https://laboutique.edpsciences.fr/produit/1353/9782759831036/solutions-to-linear-matrix-equations-and-their-applications 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/982/971/original/9782759831029-Solutions_to_Linear_Matrix_Equations_and_their_Applications_couv-sofedis.jpg 17 14 20240913T181941+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20230720 01 00 20230720 19 00 20230720 2026 06 3052868830012 01 WORLD 13 03 9782759831029 15 9782759831029 06 03 9782759831036 15 9782759831036 WORLD 08 EDP Sciences & Science Press 04 01 00 20230720 03 01 D1 EDP Sciences 31 04 05 01 02 1 00 65.99 01 5.50 3.44 EUR 04 06 01 02 1 00 231.99 01 5.50 3.44 EUR 01 04 06 01 02 1 00 255.99 01 5.50 13.35 USD 01