Linear Algebra and theorems : A Review

Abstract

Linear algebra owes its origins to the use of vectors in Cartesian two- and three-dimensional space. Vectors are described as a kind of line segment that is governed by both magnitude and direction. The first real vector space is formed by using vectors to represent physical components such as forces and then adding and multiplying them with scalars. Nowadays, it is feasible to learn linear algebra in any number of dimensions. It is a vector space of size n. Most of the useful results from 2- and 3-space may be expanded in these higher-dimensional spaces. Because they are invisible to the human eye, the n-space vectors and n-tuples are useful for describing data. Using vectors as n-tuples (ordered lists of n components), it is possible to summarise and manage data efficiently. 8-dimensional vectors or 8-tuples may be used to represent the Gross National Product of eight countries in economics.