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The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.

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Integral of the entrywise square of the exponential of a matrix

You can do something. Here's a computation for diagonalizable $A$. Let $A=BDB^{-1}$ and let the elements of $D$ be $-\lambda_1,\ldots,-\lambda_d$. Then \begin{align*} \int_0^\infty (e^{At})_{ij}^2\,d …
Anthony Quas's user avatar
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