Weinstein-Aronszajn identity

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English

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Weinstein-Aronszajn identity

Etymology

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Proper noun

the Weinstein-Aronszajn identity

(mathematics) An identity stating that if $A$ and $B$ are matrices of size $m \times n$ and $n \times m$ respectively (either or both of which may be infinite) then, provided $AB$ (and hence, also $BA$ ) is of trace class, $\det(I_{m}+AB)=\det(I_{n}+BA),$ where $I_{k}$ is the $k \times k$ identity matrix.

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