# What is the name for a function of a matrix that changes the matrix size?

I have a set of functions that map square matrices with $n$ rows and columns to square matrices with $k < n$ rows and columns. Is there a name for this property? I know that 'projection' would be the wrong word. Also I don't mean that the function only changes the size, it might also do other things.

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Are you mapping a matrix to a square submatrix? – Rahul Nov 9 '10 at 22:00
Not necessarily, but I would like 'taking a square submatrix' to be in the set of functions whose name I'm looking for. – lolol Nov 9 '10 at 22:25
I posted a new question, asking for a list of names of more specific functions. – lolol Nov 9 '10 at 22:29

Well, projection could be the right word, depending on what you want to do with the matrices. Note that matrices with $n$ rows and $m$ columns form a vector space of dimension $n \times m$. If you now restrict to matrices of $k < n$ rows, you can treat them as a $k \times m$-dimensional subspace of the original vector space, having entries in rows $i > k$ set to zero.
Also note that the dual operation of reducing the number columns might be called a restriction. This comes from the fact that you can treat $n \times m$ dimensional matrix as a representation of an operator mapping $m$-dimensional vector space to a $n$-dimensional vector space and reducing number of columns restricts this operator to a subspace of the original vector space.