The revised edition of the book fills in the urgent need of a treatise on the fundamental laws of operation with numbers so that the readers can understand points of similarity and difference between the Algebra of Matrices and of numbers. The subject is equally important to mathematical disciplines such as Geometry and Modern Algebra and to sciences. The book provides a well-rounded and complete account of important concepts of Group, Ring, Field Isomorphism, Equivalence, Congruence and reduction of real quadratic and Hermitian forms to canonical form. Elementary treatment of Vector spaces and linear independence and dependence of vector systems helps in discussing Ranks of matrices and in formulation of results of a system of equations and characteristic vector of a matrix. Illustration of every idea and theorem with abundant solved examples and lucid language are the unique features of this legendary textbook. It is a must read for Mathematics and Science students of undergraduate programmes. Aspirants trying for competitive examinations will also find the book equally useful.
1. Fundamental Concepts, 2. Algebra of Matrices, 3. Determinants, 4. Rank of a Matrix, 5. Vector Spaces of n-Tuples and Their Linear Transformations, 6. Systems of Linear Equations, 7. Quadratic Forms and Congruence of Matrices, 8. Quadratic Forms in the real field, 9. Hermitian Matrices and Forms, 10. Orthogonal Matrices: Unitary Matrices, 11. Characteristic Roots and Characteristic Vectors of a Matrix, 12. Orthogonal and Unitary Reductions of Quadratic Forms, 13. Similarity of Matrices • Appendices: I. Application to Geometry. Classification of Quadrics, II. Application to Graph Theory