Elementary Linear Algebra

Devi Prasad.: Instruction Division Birla Institute of Technology and Science, Pilani

Preface to the Second Edition / Preface to the First Edition / Matrices and Algebraic Structure: Definition / Addition and Multiplication of Matrices / Transpose of a Matrix / Matrices of Complex Numbers / Groups / Rings / Field / Exercise Set 1 / System of Linear Equations - Solution by Graphs and Elementary Row Operations / Row Reduced Echelon Form / Consistency of the Linear System / Non-sigular Matrices and Determinant Values / Inverse of a Matrix / Exercise Set 2 / Vector Spaces - Vector spaces / Subspace / Linear Dependence and Independence / Basis and Dimension / Exercise Set 3 / Linear Transformations - Linear Transformations / Null and Range Spaces / Inverse Linear Transformation / More About Linear Transformations / Matrices Related to Linear Transformations / Rank of Matrix / Exercise Set 4 / Eigenvalues and Eigenvectors - Eigenvalues and Eigenvectors / Gershgorin Circle Theorem / Diagonalization of a Matrix / Diagonalization of Symmetric Matrices/ Quadratic Forms / Exercise Set 5 / Inner Product - Inner Product / Orthogonality / Gram-Schmidt Orthogonalization / Inner Product Spaces / Exercise Set 6 / Index.