I am asked to write a linear map as a matrix with respect to a given canonical basis. The basis is

$b = \left \{ \begin{bmatrix} 1 \\ 0 \end{bmatrix} , \begin{bmatrix} 0 \\ 1 \end{bmatrix} \right \} $.

The map is given by $\phi: \mathbb{R}^2 \rightarrow \mathbb{R^2}$; $(x,y) \rightarrow (x+y, x-y)$.

I know that $\phi$ as a matrix is $\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$.

Any help would be nice. Thank you for your time.


The column vectors of the matrix of $\phi$ are the images of the basis vectors under $\phi$. For example the image of the first basis vector is $\phi\begin{pmatrix}1\\ 0\end{pmatrix}=\begin{pmatrix}1+0\\ 1-0\end{pmatrix}=\begin{pmatrix}1\\ 1\end{pmatrix}$, which is the first column of the matrix of $\phi$.

  • $\begingroup$ Ah yes, very good. Thank you very much :) $\endgroup$ – Calculus08 Jan 22 '14 at 18:12
  • $\begingroup$ Your'e welcome. $\endgroup$ – Michael Hoppe Jan 22 '14 at 18:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.