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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