Gram product ($T^{\top }T\text{ or }T{T}^{\top }$)

A real matrix product giving pairwise dot products of columns, for $T^{\top }T$, or rows, for $T{T}^{\top }$. It is a positive semidefinite matrix. The kernel of a Gram product is determined by the corresponding factor, which makes these products useful for converting a zero quadratic form into an exact null space condition.