# What's the name of this matrix?

Consider you have a rectangular matrix $$X$$ whose columns are vectors with some meaning, i.e. sampled signals.

If you evaluate the product $$G=X^H X$$ you obtain the Gramian matrix $$G$$.

If you evaluate the product $$M=X X^H$$, what is the name of the $$M$$ matrix? Does it have a particular name?

The entries of the Gramian matrix are the inner products of the columns of $$X$$, whereas the entries of $$M$$ are the inner products of the rows of $$X$$. Equivalently, $$M$$ is the Gramian matrix of $$X^H$$.