Let U & V be n-dimensional vector spaces, and f:U-->V is a linear transformation. Prove that if dimension of f:U-->V is equal to n and dimension of image of f is equal to n, then f is an isomorphism.

Thanks.(Nod)

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- July 12th 2012, 05:58 AMbertreyesLinear Algebra Problem, isomorphism
Let U & V be n-dimensional vector spaces, and f:U-->V is a linear transformation. Prove that if dimension of f:U-->V is equal to n and dimension of image of f is equal to n, then f is an isomorphism.

Thanks.(Nod)