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Let V and V' be n and m dimensional vector spaces over a field FE T

Let V and V' be n and m dimensional vector spaces over a field FE T

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 43EQ
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Theorem 5. Let V and V' be n and m dimensional vector spaces over a field FE Then for given bases B and B' of V and V respectively, the function assigning to each linear transforma- tion t : V → V" its matrix M (t) relative to bases B, B' is an isomorphism between the vector space Hom (V, V') and the space F™*n of all m×n matrices over F i.e. Hom (V, V') =Fmxn
Transcribed Image Text:Theorem 5. Let V and V' be n and m dimensional vector spaces over a field FE Then for given bases B and B' of V and V respectively, the function assigning to each linear transforma- tion t : V → V" its matrix M (t) relative to bases B, B' is an isomorphism between the vector space Hom (V, V') and the space F™*n of all m×n matrices over F i.e. Hom (V, V') =Fmxn
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