(1) Let (V₁, ||- ||1₁) and (V₂, ||- ||₂2) be two normed spaces over F and let V = V₁ × V₂ show that ||. ||: V = V₁ × V₂ → R defined as ||(x, y) || = ||x||₁ + ||y||2 is a norm on V.
(1) Let (V₁, ||- ||1₁) and (V₂, ||- ||₂2) be two normed spaces over F and let V = V₁ × V₂ show that ||. ||: V = V₁ × V₂ → R defined as ||(x, y) || = ||x||₁ + ||y||2 is a norm on V.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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