R. Merris, Extensions of the Minkowski determinant theorem, Portugaliae Math. 38 (1979), 149-153. AMS Abstracts 2 (1981), 62. Math. Reviews 84c:15009. Research supported by NSF grant MCS 77-28437.

Let d be the generalized matrix function based on a permutation group G of degree m and some (complex) irreducible character of G. Then

d([A+B]^[1/m]) >= d(A^[1/m]) + d(B^[1/m])

for all m-by-m positive definite hermitian matrices A and B. This extension of the Minkowski determinant theorem to all generalized matrix functions had previously been obtained [only] for the case in which A and B commute. The proof relies heavily on results of T. Ando.

Despite the nominal publication date, this article did not actually appear until 1982.

Among the publications citing this article are:

  • R. Bhatia and C. Davis, Concavity of certain functions of matrices, Linear & Multilinear Algebra 17 (1985), 155-164.
  • T. Ando, Manorizations and inequalities in matrix theory, Linear Algebra Appl. 199 (1994), 17-67.