Linear Algebra Done Right · Problem 9D.2

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · tensor-products

Problem

Give an example of six distinct vectors v1,v2,v3,w1,w2,w3v_1, v_2, v_3, w_1, w_2, w_3 in R3\mathbf{R}^3 such that v1⊗w1+v2⊗w2+v3⊗w3=0v_1 \otimes w_1 + v_2 \otimes w_2 + v_3 \otimes w_3 = 0 but none of v1⊗w1,v2⊗w2,v3⊗w3v_1 \otimes w_1, v_2 \otimes w_2, v_3 \otimes w_3 is a scalar multiple of another element of this list.

Related theory

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