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- February 7th 2009, 04:17 AM #1
## Diemsion of Hom

I started by making a basis of U and a basis of V.

Transforming the basis of U by T gives . These vectors may not be linearly independent so sifting them gives:

where . Let which gives me the basis of V.

Is this the correct way to start? I really can't see another way of doing this question.

EDIT: Sorry for mistyping "Dimension" as the title.

- February 7th 2009, 08:59 AM #2

- February 7th 2009, 10:43 AM #3

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Let U and V be vector spaces of dimensions n and m over K, and let be the vector space over K of all linear maps from U to V.

Find the dimension and describe a basis of .

- February 8th 2009, 04:10 AM #4

- February 8th 2009, 12:19 PM #5

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- February 8th 2009, 01:21 PM #6