Ebook: Matrices: Theory and Applications

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.

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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the ?cole Normale Sup?rieure de Lyon.

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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the ?cole Normale Sup?rieure de Lyon.
Content:
Front Matter....Pages 1-1
Elementary Linear and Multilinear Algebra....Pages 1-14
What Are Matrices....Pages 15-30
Square Matrices....Pages 31-68
Tensor and Exterior Products....Pages 69-81
Matrices with Real or Complex Entries....Pages 83-108
Hermitian Matrices....Pages 109-125
Norms....Pages 127-148
Nonnegative Matrices....Pages 149-162
Matrices with Entries in a Principal Ideal Domain; Jordan Reduction....Pages 163-181
Exponential of a Matrix, Polar Decomposition, and Classical Groups....Pages 183-205
Matrix Factorizations and Their Applications....Pages 207-223
Iterative Methods for Linear Systems....Pages 225-245
Approximation of Eigenvalues....Pages 247-275
Back Matter....Pages 271-271

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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the ?cole Normale Sup?rieure de Lyon.
Content:
Front Matter....Pages 1-1
Elementary Linear and Multilinear Algebra....Pages 1-14
What Are Matrices....Pages 15-30
Square Matrices....Pages 31-68
Tensor and Exterior Products....Pages 69-81
Matrices with Real or Complex Entries....Pages 83-108
Hermitian Matrices....Pages 109-125
Norms....Pages 127-148
Nonnegative Matrices....Pages 149-162
Matrices with Entries in a Principal Ideal Domain; Jordan Reduction....Pages 163-181
Exponential of a Matrix, Polar Decomposition, and Classical Groups....Pages 183-205
Matrix Factorizations and Their Applications....Pages 207-223
Iterative Methods for Linear Systems....Pages 225-245
Approximation of Eigenvalues....Pages 247-275
Back Matter....Pages 271-271
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