Compression of a linear operator
= Compression of a linear operator
If $V$ is a subspace of a space with an <inner product> and $P_V$ is its <orthogonal projection onto a finite-dimensional subspace>[orthogonal projection], the compression of an operator $A$ to $V$ is
$$
P_VA|_V:V\longrightarrow V.
$$
If the columns of $Z$ are an <orthonormal basis> of $V$, its matrix in that basis is $Z^*AZ$.