- 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.