Weighted l₁ norms for matrices

Abstract

Let W =(W_ij ) be a fixed m × n weight matrix, and let the W-weighied l₁ , norm on C_m×n be defined by

Given weight matrices U,V,W, of orders m × r r × n and m × n, respectively, we begin by proving that a constant μ > 0 satisfies

In the second part of this note we restrict attention to a single weighted l₁ norm on C _n×n ,and show that

We conclude that may be quadrative without being multiplicative on C _n×n .

^∗Research sponsored in part by the Fund for the Promotion of Research at the Technion

^∗Research sponsored in part by the Fund for the Promotion of Research at the Technion

Notes

^∗Research sponsored in part by the Fund for the Promotion of Research at the Technion