Cases of equality for the spectral norm submultiplicativity of the hadamard product

Abstract

In this note, we characterize those pairs of nonzero r-by-d complex matrices that satisfy N ₂(A ∘ B) = N ₂(A)N ₂(B), in which N ₂(·) is the spectral norm and · is the Hadamard product.

^*This work was supported in part by National Science Foundation grant DMS-88-02836, a grant from the National Security Agency and Office of Naval Research contract N00014-87-K-0012.

^*This work was supported in part by National Science Foundation grant DMS-88-02836, a grant from the National Security Agency and Office of Naval Research contract N00014-87-K-0012.

Notes

^*This work was supported in part by National Science Foundation grant DMS-88-02836, a grant from the National Security Agency and Office of Naval Research contract N00014-87-K-0012.