11-136 Sterling K. Berberian

"Expansion of a determinant by cofactors, revisited" (73K, PDF uuencoded) Sep 25, 11

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Abstract. The proof that a determinant of an n x n matrix can be computed as a linear combination of cofactors is usually made by organizing the n! terms in the development of the determinant into the desired linear combination. Instead, the present proof demonstrates that the desired linear combination formula, regarded as a function of the column vectors of a matrix, has the properties that characterize the determinant function, namely, that it is an alternate multilinear function of the column vectors that assigns the value 1 to the identity matrix; it therefore assigns to every n x n matrix its determinant. The pdf file (cofactor.pdf) contains 54,154 bytes.

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