Extremal Properties of Hermitian Matrices. II
Marvin D. Marcus, B. N. Moyls, R. Westwick · Canadian Journal of Mathematics · 1959
Let H be an n-square Hermitian matrix with eigenvalues h1 ≥ h2 ≥ . . . ≥ hn. Fan (2) showed that 1 k — 1,2, … , n, where the max and min are taken over all sets of k orthonormal (o.n.) vectors in unitary w-space Vn. Marcus and McGregor (3) have generalized this result in the case that H is non-negative Hermitian. For vectors X1, … , xr r ≤ n, in Vn, let X1 Λ X2 Λ … Λ xT denote the Grassmann exterior product of the xt; it is a vector in Vm,, where