Some more on a conjecture of marcus and wang
Chi Fai Chan · Linear and Multilinear Algebra · 1989
Let denote the generalized matrix function associated with a subgroup H of m and an irreducible complex character χ of H. The purpose of this note is to show that if χ is the principal character, then for any n-square complex matrix A where nm, that for each n-by-m complex matrix U satisfying U ∗ U=Im implies A=0. Furthermore, this property characterizes the principal characters of the subgroups of Sm .