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Results tagged with matrix-exponential
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user 1898
The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
6
votes
Accepted
Kronecker product: Is it possible to simplify this product $e^{-A} \otimes e^{A}$ where $A$ ...
One can diagonalize your $A = VDV^{-1}$ explicitly; the closed formulas are here for instance.
Once you have those matrices, you can write the orthogonal eigendecomposition
$$
\exp(-A) \otimes \exp(A) …
- 20.2k
5
votes
Fast Upper Triangular Matrix Exponentiation
You probably want the Schur-Parlett method for computing matrix functions. It is a method to compute a generic function of a triangular matrix. Essentially, you apply the function to its diagonal elem …
- 20.2k
12
votes
Matrix elements of exponential of tridiagonal matrices
Yes! Most methods to compute exponentials of large sparse matrices are based on computing directly $\exp(A)b$ for a given vector $b$ rather than the full matrix $\exp(A)$. Just take $b$ as a vector of …
- 20.2k
5
votes
Accepted
Attempts to define a matrix exponential over (as much as possible) general fields
You can give an equivalent definition of the matrix exponential. or any matrix function $f$, using the Jordan form. If $A = VJV^{-1}$, and $J$ is the direct sum of diagonal blocks of the form
$$
J_i = …
- 20.2k