Elementary Linear Algebra is a well-organized, lucidly written text, introducing readers to Matrices, Groups, Rings, Fields, System of linear equations, Computation of non-singular matrices and determinant value of a matrix , Vector spaces, Row reduction method of linear dependence and independence, Linear transformations, Eigen values, Eigen vectors, Kayley Hamilton Theorem of Eigen values, Eigen vectors, Inner Product spaces. In addition, the book presents the subject in a simple manner for easy understanding. A large number of illustrated examples are given to clarify the theoretical concepts with unsolved problems for practice to enhance the presentation of the material. NEW TO THE THIRD EDITION: Sections on: • Isomorphic transformation • Bilinear transformation • Linear Functional • Adjoint Operators • Self-adjoint Operators Normed • Banach and Hilbert Spaces

Preface to the Third 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-singular 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 and Some Spaces – Inner Product / Orthogonality / Gram-Schmidt Orthogonalization / Inner Product Spaces / The Adjoint of a Transformation / Bilinear Transformation / Normed Spaces, Banach Spaces / Hilbert Spaces / Exercise Set 6 / Index.

Undergraduate Students