Linear Algebra Done Right · Problem 9D.3

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · tensor-products

Problem

Suppose that v1,…,vmv_1, \ldots, v_m is a linearly independent list in VV. Suppose also that w1,…,wmw_1, \ldots, w_m is a list in WW such that v1⊗w1+⋯+vm⊗wm=0.v_1 \otimes w_1 + \cdots + v_m \otimes w_m = 0. Prove that w1=⋯=wm=0w_1 = \cdots = w_m = 0.

Related theory

Browse the problem library