Preliminaries

Abstract

Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces. Linear algebra is commonly restricted to the case of finite-dimensional vector spaces, while the peculiarities of the infinite-dimensional case are traditionally covered in the functional analysis. We use the following notations: $\bullet$ $\mathbb {N}=\{0,1,2,\ldots \}$ is the set of all natural numbers. $\bullet$ $\mathbb {R}$ is the set of all real numbers. $\bullet$ $\mathbb {Z}=\{\ldots ,-1,0,1,\ldots \}$ is the set of integers.