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Results tagged with matrix-exponential
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user 13650
The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
14
votes
Question on whether, "An entire function, nowhere zero, has an entire logarithm," holds for ...
Counterexample: Consider the entire function $$ A(z) = \pmatrix{e^z & 0\cr
z & 1\cr}$$
An entire logarithm of $A(z)$ must have eigenvalues $z + 2\pi i n$ and $2 \pi i m$ for …
- 54.2k
4
votes
Accepted
Bounds on Matrix Exponential
$\|C(k)\|$ can be arbitrarily large, since e.g. you can add some large integer multiple of $2\pi i I$ without changing $e^{C(k)}$. If you want to try to avoid this, you might specify that $C(k)$ is t …
- 54.2k
7
votes
How to prove this determinant is positive?
Here is a counterexample with $N=3$. Consider the matrices
$$ B_1 = \log(t) \pmatrix{0 & 4\cr -1 & 0\cr}, B_2 = \log(t) \pmatrix{-2 & 2\cr 1 & 2\cr}, B_3 = \log(t) \pmatrix{4 & -2\cr -2 & 1\cr}$$
whe …
- 54.2k