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Fundamentals of Linear Algebra / by Chahal, J.S

Table of Contents: “…-- Rudimentary Set Theory -- Cartesian Products -- Relations -- Concept of a Function -- Composite Functions -- Fields of Scalars -- Techniques for Proving Theorems -- 2 Matrix Algebra -- Matrix Operations -- Geometric Meaning of a Matrix Equation -- Systems of Linear Equation -- Inverse of a Matrix -- The Equation Ax=b -- Basic Applications -- 3 Vector Spaces -- The Concept of a Vector Space -- Subspaces -- The Dimension of a Vector Space -- Linear Independence -- Application of Knowing dim (V) -- Coordinates -- Rank of a Matrix -- 4 LinearMaps -- Linear Maps -- Properties of Linear Maps -- Matrix of a Linear Map -- Matrix Algebra and Algebra of Linear Maps -- Linear Functionals and Duality -- Equivalence and Similarity -- Application to Higher Order Differential Equations -- 5 Determinants -- Motivation -- Properties of Determinants -- Existence and Uniqueness of Determinant -- Computational Definition of Determinant -- Evaluation of Determinants -- Adjoint and Cramer's Rule -- 6 Diagonalization -- Motivation -- Eigenvalues and Eigenvectors -- Cayley-Hamilton Theorem -- 7 Inner Product Spaces -- Inner Product -- Fourier Series -- Orthogonal and Orthonormal Sets -- Gram-Schmidt Process -- Orthogonal Projections on Subspaces -- 8 Linear Algebra over Complex Numbers -- Algebra of Complex Numbers -- Diagonalization of Matrices with Complex Eigenvalues -- Matrices over Complex Numbers -- 9 Orthonormal Diagonalization -- Motivational Introduction -- Matrix Representation of a Quadratic Form -- Spectral Decompostion -- Constrained Optimization-Extrema of Spectrum -- Singular Value Decomposition (SVD) -- 10Selected Applications of Linear Algebra -- System of First Order Linear Differential Equations -- Multivariable Calculus -- Special Theory of Relativity -- Cryptography -- Solving Famous Problems from Greek Geometry -- Answers to Selected Numberical Problems -- Bibliography -- Index.…”
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