Definition and Feature of Determinant of a Matrix

• 1、School of Mathematics and Computing Science of ShenZhen University

Abstract：Determinant is important in theory and calculation of linear algebra. Now used determinant is defined on square matrix, and a matrix which is not square matrix has not good definition of determinant. This paper gives a generalized definition of determinant of any matrix. In the definition, any matrix has row determinant and column determinant. When the matrix is square, its two determinants are same which also equal to determinant now used. If the matrix’s row number is larger than its column number, its row determinant is defined as 0, and on this time, if the rank of matrix is equal its column number, its column determinant has value of highest no-zero largest order determinant, otherwise the column determinant is 0. If a matrix’s row number is less than its row number, its row determinant and column determinant are column determinant and row determinant of its transpose.

Keywords： linear algebra determenant linear system