| Description |
1 online resource (412 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- 1. Vectors and Matrices -- 1.1. Introduction -- 1.2. Scalars and Vectors -- 1.3. Introduction to Matrices -- 1.4. Types of Matrices -- 1.5. Elementary Operations and Elementary Matrices -- 1.6. Determinants -- 1.7. Inverse of a Matrix -- 1.8. Partitioning of Matrices -- 1.9. Advanced Topics: Pseudo Inverse and Congruent Inverse -- 1.10. Conclusion -- 2. Linear System of Equations -- 2.1. Introduction -- 2.2. Linear System of Equations -- 2.3. Rank of a Matrix -- 2.4. Echelon Form and Normal Form |
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2.5. Solutions of a Linear System of Equations -- 2.6. Cayley-Hamilton Theorem -- 2.7. Eigen-values and Eigen-vectors -- 2.8. Singular Values and Singular Vectors -- 2.9. Quadratic Forms -- 2.10. Conclusion -- 3. Vector Spaces -- 3.1. Introduction -- 3.2. Vector Space and Subspaces -- 3.3. Linear Independence, Basis and Dimension -- 3.4. Change of Basis-Matrix -- 3.5. Linear Transformations -- 3.6. Matrices of Linear Transformations -- 3.7. Inner Product Space -- 3.8. Gram-Schmidt Orthogonalization -- 3.9. Linking Linear Algebra to Differential Equations -- 3.10. Conclusion |
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4. Numerical Methods in Linear Algebra -- 4.1. Introduction -- 4.2. Elements of Computation and Errors -- 4.3. Direct Methods for Solving a Linear System of Equations -- 4.4. Iterative Methods -- 4.5. Householder Transformation -- 4.6. Tridiagonalization of a Symmetric Matrix by Plane Rotation -- 4.7. QR Decomposition -- 4.8. Eigen-values: Bounds and Power Method -- 4.9. Krylov Subspace Methods -- 4.10. Conclusion -- 5. Applications -- 5.1. Introduction -- 5.2. Finding Curves through Given Points -- 5.3. Markov Chains -- 5.4. Leontief 's Models -- 5.5. Cryptology |
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5.6. Application to Computer Graphics -- 5.7. Application to Robotics -- 5.8. Bioinformatics -- 5.9. Principal Component Analysis (PCA) -- 5.10. Big Data -- 5.11. Conclusion -- 6. Kronecker Product -- 6.1. Introduction -- 6.2. Primary Matrices -- 6.3. Kronecker Products -- 6.4. Further Properties of Kronecker Products -- 6.5. Kronecker Product of Two Linear Transformations -- 6.6. Kronecker Product and Vector Operators -- 6.7. Permutation Matrices and Kronecker Products -- 6.8. Analytical Functions and Kronecker Product -- 6.9. Kronecker Sum -- 6.10. Lyapunov Function -- 6.11. Conclusion |
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7. Calculus of Matrices -- 7.1. Introduction -- 7.2. Derivative of a Matrix Valued Function with Respect to a Scalar -- 7.3. Derivative of a Vector-Valued Function w.r.t. a Vector -- 7.4. Derivative of a Scalar-Valued Function w.r.t. a Matrix -- 7.5. Derivative of a Matrix Valued Function w.r.t. its Entries and Vice versa -- 7.6. The Matrix Differential -- 7.7. Derivative of a Matrix w.r.t. a Matrix -- 7.8. Derivative Formula using Kronecker Products -- 7.9. Another Definition for Derivative of a Matrix w.r.t. a Matrix -- 7.10. Conclusion -- 8. Linear Systems of Differential Equations |
| Notes |
Description based upon print version of record |
|
8.1. Introduction |
| Form |
Electronic book
|
| Author |
Deo, Sadashiv G
|
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Khandeparkar, Ramakrishna
|
| ISBN |
9781351014946 |
|
1351014943 |
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