Representing Matrix

Prof. Dr. Christian Bär
University of Potsdam, Germany

We consider the linear map $\varphi_Z:\mathbb{R}^n\to\mathbb{R}^m$ given by $\varphi(x)=Z\cdot x$. Here, $Z$ is a given matrix. Moreover, we are given ordered bases $A=(a_1,\ldots,a_n)$ of $\mathbb{R}^n$ and $B=(b_1,\ldots,b_m)$ of $\mathbb{R}^m$. You should now compute the matrix $M^A_B(\varphi_Z)$ which represents $\varphi_Z$ w.r.t. the basis $A$ and $B$, respectively.

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