Determinants

A determinant of a square matrix is any number that is the product of the diagonal entries of a diagonal matrix equivalent to it. The main objective of this chapter is to show that a square matrix has only one determinant; in other words, if two diagonal square matrices are equivalent, then the product of the diagonal entries of one is the same as the product of the diagonal entries of the other. Once this theorem is proved, we will speak of the determinant of a square matrix, not a determinant.