Theory of Matrices

The theory of matrices is a fundamental branch of mathematics that deals with the study of matrices which are rectangular arrays of numbers symbols or expressions arranged in rows and columns. Matrices find wide applications in various fields such as physics computer science engineering and economics. The study of matrices includes operations like addition subtraction multiplication and inversion each with its own set of rules and properties. One of the key concepts in matrix theory is the determinant a scalar value derived from a square matrix that provides important information about the matrix's properties such as its invertibility. Matrix theory also encompasses the study of systems of linear equations where matrices are used to represent the coefficients of the variables. The theory provides methods for solving these systems such as Gaussian elimination and matrix inversion which are crucial in many practical applications.The theory of matrices is a broad and foundational area of mathematics with diverse applications across various disciplines. Its study not only provides valuable tools for solving practical problems but also deepens our understanding of fundamental mathematical concepts. The book Theory Of Matrices covers essential topics such as matrix algebra determinants eigenvalues eigenvectors and canonical forms. It also explores applications in various fields including linear transformations systems of linear equations and numerical analysis. Designed for both undergraduate and graduate students the book provides rigorous mathematical proofs alongside practical examples.