The Hadamard product $A \odot B$ gives the element-wise multiplication of matricies $A$ and $B$.
How do I denote the raising a matrix to the power $n$, element-wise?
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Wikipedia's Hadamard Analogous operations gives the following notation for raising each element of $A$ to the power of $n$:
This is called the "Hadamard power" for which Google has 2,960 results, or perhaps "Hadamard exponentiation" (19 google results).