DETERMINANTS AND MATRICES
Selçuk Ş. Bayın · 2019
In many areas of mathematical analysis, we encounter systems of ordered sets of elements, which could be sets of numbers, functions, or even equations. In this chapter, the authors present a formal treatment of matrices and determinants and their applications to systems of linear equations. They introduce determinants that play a very important role in the theory of matrices. Determinants are scalars associated with square matrices. Evaluation of determinants by using the basic definition is practical only for small orders, usually up to 3 or 4. If two rows or columns of a square matrix are proportional, then its determinant is zero. If two rows or columns of a determinant are interchanged, then the value of the determinant reverses sign. The transpose of a matrix is obtained by interchanging its rows and columns, and it is denoted by AT or A. Programs like Matlab, Mathematica, Maple, etc., include matrix diagonalization and inverse matrix calculation routines.