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A generalization of the Cayley-Hamilton theorem. (English)
Am. Math. Mon. 119, No. 4, 340-342 (2012).
The author proves that the determinant of the matrix $[b_{ij}A - a_{ij}B]_{n\times n}$, which is regarded as an $n\times n$ block matrix with pairwise commuting entries and where $A = [a_{ij}]_{n\times n}$, $B = [b_{ij}]_{n\times n }$ are two commuting square matrices of order $n$ over an arbitrary commutative ring, is exactly equal to the $n\times n$ zero matrix. If $B$ is the identity matrix, then the result is equivalent to the Cayley-Hamilton theorem.
Reviewer: Costică Moroşanu (Iaşi)
Classification: H65