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  "body": "\n## Summary\n\nA matrix function extends a scalar function $f$ to square matrices, giving a matrix $f(A)$ for a matrix $A$.\nFor a function given by a [[power series|0MZB06ST2B]], $f(A)$ is obtained by putting $A$ into the series.\nThe [[matrix exponential|020M04FN1H]], the [[logarithm of a matrix|FS339MCFEQ]] and the [[square root of a matrix|63FAKMYZ2E]] are the main examples.\nThey are used to solve linear differential equations and in numerical analysis, control theory and quantum mechanics.\n\n## Explanations\n\n### L1 human\n\nMany functions are sums of powers, like $e^x = 1 + x + x^2/2 + \\cdots$.\nPowers of a square matrix make sense, so one can put a matrix in place of $x$.\nFor a diagonal matrix, this simply applies $f$ to each diagonal entry.\nFor a general matrix, $f(A)$ acts on each eigenvector of $A$ by multiplying it by $f$ of the eigenvalue.\n",
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