On Eigenvalues of Symmetric Matrices with Psd Principal Submatrices
On Eigenvalues of Symmetric Matrices with Psd Principal Submatrices
We investigate convexity properties of the set of eigenvaluetuples of n × n real symmetric matrices, whose all k × k (where k ≤ n isfixed) minors are positive semidefinite. We prove that the set λ(𝒮 n,k ) ofeigenvalue vectors of all such matrices is star-shaped with respect to thenonnegative …