Rapidsol Algebra I (Pbi. U.)

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The present book provides a comprehensive treatment of the concepts and topics by giving a vast variety of examples fully solved. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for a better understanding of the subject.


Hermitian, Skew-Hermitian, Orthogonal and Unitary matrices. Elementary operation on matrices. Inverse of a matrix using Gauss Jordan Method. Linear independence of row and column vectors, Row rank, Column rank and their equivalence. Eigen values, Eigen vectors and the characteristic equation of a matrix, Properties of eigen values for special type of matrices, Diagonalization, Cayley-Hamilton theorem. Consistency of a system of linear equations.

       Relations between roots and coefficients of a general polynomial, Transformation of equation. Descartes’ rule of signs, Solution of cubic equations, Biquadratic equations and their solution. De Moivre’s theorem and its application, Direct and inverse circular functions, hyperbolic and logarithmic functions. Summation of Series.

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