Do you have any idea what matrix space is? Can someone explain what matrix space is by a given example. Is it a set of number?
 A: Matrix spaces are vector spaces: See the entry for Vector Spaces in Wikipedia, and you'll find that a matrix space is a vector space.

"A vector space is a mathematical structure  formed by a collection of elements called vectors [and in this context, vectors can be matrices, polynomials...], which may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers..."

A matrix space, like vector spaces in general, consists of a set of $M_{m\times n}$ of matrices whose entries are from a field of numbers, which is closed under matrix addition and scalar multiplication. See Basic Operations: Matrices
An example would be the set of all real $2\times 2$ matrices together with matrix addition and scalar multiplication.
A: The vector space of matrices (with entries from some field F) of a given order would be a matrix space(over that field), denoted by $ M(m\times n,F) $.  I am assuming you know what a Vector space is.You can just put $ m=n=2 $ and $ F= \mathbb R $ get a good picture of such spaces yourself. I hope this is what you are looking for.
