Hadamard power
= Hadamard power
{c}
{title2=$X^{\circ k}$}
= Entrywise matrix power
{synonym}
For integer $k\geq1$, the entrywise power has entries $X_{ij}^k$ and equals the repeated <Hadamard product>. The zero power is the all-ones <matrix>, even at zero entries, because it represents the constant function one. Every nonnegative integer <Hadamard power> of a <positive semidefinite matrix> is <positive semidefinite> by the <Schur product theorem>. It is not an ordinary <matrix> power.