If V and W are of dimension m and n respectively over F then Hom(V, W) is of dimension mn over F

Definition of Inner Product Space and a proof of a lemma using its conditions.

Independence, Basis, and Dimension

If A is an algebra, with unit element, over F then A is isomorphic to a subalgebra of A(V)

Lecture 8 dim[L(V,W)]=dimV.dimW, if both have finite dimension

Prove that homomorphism of V, W is a vector space over F under suitable operation.

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9. Independence, Basis, and Dimension

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