Matrices and Related Topics

Abstract

The aim of this chapter is to discuss the basic operations on matrices, to introduce the notions of linear (in)dependence of elements in $\mathbb {R}^k$, of a basis of $\mathbb {R}^k$ and of coordinates of an element in $\mathbb {R}^k$ with respect to a basis. Furthermore, we extend the notion of the determinant of $2\times 2$ matrices, introduced at the end of Sect. 1.2, to square matrices of arbitrary dimension and characterize invertible square matrices as being those with nonvanishing determinant.