# Basis and Transformation matrix

by yunadesu   Last Updated September 12, 2019 04:20 AM

Suppose I have two vector spaces $$A,B$$ that are of dimensions $$n,m$$ respectively, and $$T: A \to B$$ is a linear map. I'm asked to show that there exists order bases $$P \subset A$$, $$Q \subset B$$, $$d \leq \min\{n,m\}$$ such that the transformation matrix of $$T$$ is of the form $$a_{ij} =1$$ if $$i=j\leq d$$, and $$a_{ij}=0$$ otherwise.

I don't know how to start the question, any hints on it?

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