The sign invariance of certain norms on
Rohan Hemasinha · Linear and Multilinear Algebra · 1993
Let denote the set of all n×1 real column vectors and let Δn denote the group of all n×n diagonal matrices over whose diagonal entries have absolute value one. A norm ∥⋅∥ on is said to be sign invariant of Given a norm ∥⋅∥ on and an m×n real matrix H of rank n on can define a norm ∥⋅∥ H on by In this note we study the following problem. If ∥⋅∥ p is the lp norm on then what conditions on H will entail that ∥⋅∥ H,p is sign invariant.