دانلود کتاب Matrix Theory and Applications for Scientists and Engineers

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Title Page
Copyright Page
Contents
Preface
Chapter 1 – Matrices
1.1 Matrices and Matrix Operations
1.2 Some Properties of Matrix Operations
1.3 Partitioned Matrices
1.4 Some Special Matrices
1.5 The State – Space Concept
Chapter 2 – Vector Spaces
2.1 Vectors
2.2 Linear Dependence and Bases
2.3 Coordinates and the Transition Matrix
Chapter 3 – Linear Transformations
3.1 Homomorphisms
3.2 Isomorphism and Vector Spaces
3.3 Linear Transformations and Matrices
3.4 Orthogonal Transformations
3.5 General Change of Bases for a Linear Transformation
Chapter 4 – The Rank and the Determinant of a Matrix
4.1 The Kernel and the Image Space of a Linear Transformation
4.2 The Rank of a Matrix
4.3 The Determinant of a Matrix
4.4 Operations with Determinants
4.5 Cramer’s Rule
Chapter 5 – Linear Equations
5.1 Systems of Homogeneous Equations
5.2 Systems of Non-Homogeneous Equations
Chapter 6 – Eigenvectors and Eigenvalues
6.1 The Characteristic Equation
6.2 The Eigenvalues of the transposed matrix
6.3 When all the Eigenvalues of A are distinct
6.4 A reduction to a Diagonal Form
6.5 Multiple Eigenvalues
6.6 The Cayley-Hamilton Theorem
Chapter 7 – Canonical Forms and Matrix Functions
7.1 Polynomials
7.2 Eigenvalues of Rational Functions of a Matrix
7.3 The Minimum Polynomial of a Matrix
7.4 Direct Sums and Invariant Subspaces
7.5 A Decomposition of a Vector Space
7.6 Cyclic Bases and the Rational Canonical Form
7.7 The Jordan Canonical Forms
7.8 Matrix Functions
Chapter 8 – Inverting a Matrix
8.1 Elementary Operations and Elementrry Matrices
8.2 The Inverse of a Vandermonde Matrix
8.3 Faddeeva’s Method
8.4 Inverting a Matrix with Complex Elements
Solutions to Problems
References and Bibliography
Index