# Questions tagged [matrix-exponential]

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

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### Question on whether, "An entire function, nowhere zero, has an entire logarithm," holds for matrix-valued entire functions as well

It is known that an entire function that is nowhere zero must be the exponential of another entire function. Does this hold for matrix-valued functions as well? That is, given a matrix-valued entire ...
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### Logarithm of a bounded operator

Let $\mathbb H$ be a Hilbert space and let $A\in \mathcal B(\mathbb H)$ such that the spectrum of $A$ does not meet a closed half-line issued from 0 in the complex plane. Then I guess that $A=\exp L$...
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### Limiting value of expectation of trace of exponential of Wishart matrix

Let $X$ be an $n \times d$ random matrix with iid entries from $N(0, 1/d)$. Let $S:=X^\top X/n$, a $d \times d$ Wishart matrix and let $T = e^{S} := \sum_{k=0}^\infty \dfrac{S^k}{k!}$ be its ...
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### Matrix logarithm of unitary factor from polar decomposition of product of positive definite matrices

This question is crossposted from Math Stackexchange here. I crosspost without much edits as I think this is the best way to phrase the question and because I received no feedback on the original post ...
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### Exponential of infinite dimensional matrix

Originally posted on Math SE but didn't get any responses. Thus, I thought I would ask here with some more details. I have a matrix originating from Master Equation for birth death process on semi ...
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### Inequality of exponentials of Banach operators

(I have moved this question from Stackexchange). Given the operators $\{A_j\}$ in a Banach algebra and a positive integer $p$, let g=\exp\left(\frac{1}{n}\sum_{j=1}^p A_j\right)\quad\...
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### Random variable matrix exponential

I am trying to find out the distribution of a matrix exponential which is a function of a random variable. My mathematics background is very limited and I hope I can receive some help from here. What ...
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