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?


1 Answer 1


Wikipedia's Hadamard Analogous operations gives the following notation for raising each element of $A$ to the power of $n$:

$$\huge{A^{\circ n}}$$

This is called the "Hadamard power" for which Google has 2,960 results, or perhaps "Hadamard exponentiation" (19 google results).

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    $\begingroup$ which may come as surprise (to me at last). For maps, the notation $f^{\circ n}$ is often used when one needs to distinguidh iteration from product, i.e., $f^{\circ 3}(x)=f(f(f(x)))$ vs. $f^3(x)=f(x)\cdot f(x)\cdot f(x)$. Then again, (non-Hadamard) matrix multiplication (and hence power) already corresponds to composition / iteration of linear maps ... $\endgroup$ Apr 23, 2018 at 5:06
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    $\begingroup$ @HagenvonEitzen Perhaps the \odot or $\odot$ operator is a better choice then? See this discussion on Hadamard notation. $\endgroup$
    – Tom Hale
    Apr 23, 2018 at 5:13

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