Various properties of symmetric matrix and anti-symmetric matrix

Matrix serves as a key tool in the study of Advanced Algebra.However in studying the transpose of matrix much focus has been given on the definition of symmetric matrix and anti-symmetric matrix while their properties have not been fully explored.As special forms of matrixes,symmetric and anti-symmetric matrix plays a key role not only in the theory of matrix but also in actual application.Properties of the two forms of special matrixes are frequently used and discussed in the study of matrix and related mathematical knowledge.This paper first presents the definition of symmetric matrix and anti-symmetric matrix and then moves on the disscussion of certain properties of them.