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Results tagged with matrix-exponential
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user 48839
The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
3
votes
Property for bounding matrix exponential
The wikipedia article you refer to is here. This indeed states that
$$
\|e^{X+Y}-e^X\| \le \|Y\| e^{\|X\|}e^{\|Y\|} \tag{1}\label{1}
$$
for any "matrix norm", and, according to the link that is given, …
- 24.2k
14
votes
How to prove this determinant is positive?
Update 1: Thanks to jjcale for pointing out a fatal flaw. Indeed $SO(n,n)$ has two components, see here, and it looks suspiciously like my $T$ below is in the wrong component. I don't really know what …
- 24.2k
4
votes
Question on whether, "An entire function, nowhere zero, has an entire logarithm," holds for ...
This is my comment above slightly expanded. Let's focus on $2\times 2$ matrices for convenience and let $A(z)$ be entire with $\det A=1$ (divide through by a holomorphic square root of $\det A$ if thi …
- 24.2k