what is a Matrix?

Question

we have all seen these collections of numbers in large brackets. But what exactly is a matrix?
Is it just a collection of scalar numbers or vectors?
I have seen in some textbooks the 'name' of the matrix given in bold letters but in some places not.

So what exactly is it?

so, its not a collection of vectors?

Answer 1

In mathematics, a matrix is any rectangular array of quantities, most typically a square N x N matrix of scalars, but not limited to. For instance, we can have a A x B x C array of vectors, or a N x M array of functions, or, as in integral transform theory, have infinite-dimensional matrices. A matrix, as defined, is presumed to have certain algebraic properties, such as additivity or associativity, but not necessarily commutativity. It's a very general concept, not necessarily involving vector spaces.

Answer 2

A matrix is an array to help organize data. Think of it as a table or chart, but one that can have operations done to it.

Answer 3

It is a tableaux or array of coefficients for a linear problem. It could be a simple system of linear equations of n variables or a system of linear differential equations.

Answer 4

It's also the name of a movie.