A function T:V→W between vector spaces V and W is called additive if T(x+y)=T(x)+T(y) for all x,y ϵ V. Prove that if V and W are vector spaces over the field of rational numbers, then any additive function from V into W is a linear transformation.
A function T:V→W between vector spaces V and W is called additive if T(x+y)=T(x)+T(y) for all x,y ϵ V. Prove that if V and W are vector spaces over the field of rational numbers, then any additive function from V into W is a linear transformation.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 1CM
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