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Results tagged with matrix-exponential
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user 18060
The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
14
votes
Accepted
exponential/logarithm for unipotent algebraic groups
This is false in characteristic $p$, no matter how large $p$ is. The counterexample is the group parameterized by
$\begin{pmatrix} 1 & t & t^p \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$
Its Lie algebr …
- 148k
10
votes
Accepted
Integral of the entrywise square of the exponential of a matrix
Inspired strongly by Anthony's answer, here is a formula that works for arbitrary $A$. Let $M$ be the $n^2 \times n^2$ square matrix given by $$M= A \otimes I_n + I_n \otimes A_n$$
i.e. in terms of in …
- 148k
9
votes
How to prove this determinant is positive?
The set of matrices of the form $e^{A_1} \dots e^{A_n}$ with $A_1, \dots , A_n$ of this form are a group. This is because it is clearly closed under multiplication and if $A$ is of this form then $-A$ …
- 148k