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Two vector spaces V and W over the field F are isomorphic if and only if there is a bijection /: VW such that f(x +y) - f(x) + S(u) for all z, y E V, and f(sar) of dimension n over Fis isomorphic to F". sf() for all rEV and s E F. Prove that a vector space

Two vector spaces V and W over the field F are isomorphic if and only if there is a bijection /: VW such that f(x +y) - f(x) + S(u) for all z, y E V, and f(sar) of dimension n over Fis isomorphic to F". sf() for all rEV and s E F. Prove that a vector space

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Two vector spaces V and W over the field F are isomorphic if and only if there is a bijection f: VW such that f(x + y) = S() + f(y) for all 2,yE V, and f(sz) = sf(x) for all r eV and s E F. Prove that a vector space of dimension n over Fis isomorphic to F".
Transcribed Image Text:Two vector spaces V and W over the field F are isomorphic if and only if there is a bijection f: VW such that f(x + y) = S() + f(y) for all 2,yE V, and f(sz) = sf(x) for all r eV and s E F. Prove that a vector space of dimension n over Fis isomorphic to F".
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