Cayley-Hamilton Theorem for mixed discriminants
نویسندگان
چکیده
The mixed discriminant of an n-tuple of n×n matrices A1, . . . , An is defined as D(A1, A2, . . . , An) = 1 n! ∑ σ∈S(n) det(A (1) σ(1), A (2) σ(2), . . . , A (n) σ(n)), where A denotes the ith column of the matrix A and S(n) denotes the group of permutations of 1, 2, . . . , n. For n matrices A1, ..., An and indeterminates λ1, . . . , λn, set Φλ1,...,λn(A1, ..., An) = D(λ1I −A1, ..., λnI −An). It is shown that ΦA1,...,An(A1, ..., An) = 0.
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