e to the A, in a New Way, Some More to Say
P. Federbush (Univ. of Michigan)
TL;DR
This paper derives explicit formulas for the exponential of a Hermitian matrix and its Fourier transform, extending known results to matrices of any size with elegant expressions.
Contribution
It introduces general explicit formulas for matrix exponentials and Fourier transforms, expanding previous small-size matrix results to arbitrary dimensions.
Findings
Formulas extend to any matrix size
Explicit expressions are elegant and practical
Useful for advanced matrix analysis
Abstract
Expressions are given for the exponential of a hermitian matrix, A. Replacing A by iA these are explicit formulas for the Fourier transform of exp(iA). They extend to any size matrix the previous results for the 2 X 2, 3 X 3, and 4 X 4 cases. The expressions are elegant and should prove useful.
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Taxonomy
TopicsMatrix Theory and Algorithms · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods