Matrix - definition
Matrix - definition
A Matrix is an ordered arrangement of numbers, symbols or mathematical expressions, stored as a rectangular array consisting of rows and columns. Each element of a matrix is defined by its position, i.e. the indices corresponding to a particular row and column. Matrices are among the basic structures in linear algebra and are widely used in applied mathematics, physics, computer science, engineering and computational science.
Formally, a matrix is a mathematical object represented by a set of elements written in a two-dimensional system, usually denoted by a capital letter, e.g. A, with the individual components denoted by symbols of the type aᵢⱼ, where i is the row index and j the column index. The size of the matrix is described as the number of rows per number of columns (m×n), which makes it possible to explicitly define the structure of the data and the rules for performing algebraic operations.
Matrices are used, among other things, to describe systems of linear equations, geometric transformations, spatial transformations, modelling the dynamics of physical systems and for analysis and signal processing. In computer science and programming, matrices form the basis for the representation of numerical data, digital images, graphs and in machine learning, where they are used in implementations of artificial intelligence and neural networks algorithms.
The basic operations performed on matrices are addition, multiplication, transpose, determinant, inverse matrix calculation and eigenoperations such as finding eigenvalues and eigenvectors. In the analysis of dynamic systems and Automation, matrices are used to write the equations of state and to describe the properties of linear systems. Their algebraic structure allows the generalisation of vector calculus to spaces of arbitrary dimension.
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