A Study of Linear Algebra and Matrices Alternative Formulations in Vector Spaces

Exploring the Applications and Structures of Vector Spaces in Mathematical Analysis

Abstract

Linear algebra and its dimension are clearly defined and the quantity of separate spatial directions approximately defines vector spaces. Naturally, in mathematical analysis, vector spaces that have functions exist as function spaces. Generally, these vector spaces have several more structures, including a topology which enables exploration of closeness and continuity issues. These topologies are more widely used described by a standard or an internal product (with a notion of distance between two vectors). In the field of mathematical analyzes, this is particularly true of Banach and Hilbert Spaces. There is increasing use of vector spaces in math, science and engineering. They are the best linear-algebraic definition in linear equation systems. They provide the basis for Fourier expansion, used in image compression, and create an environment for partial differential equations for solution technology.