Representation of a Matrix to a basis

[blackbear]

Homework Statement

This problem refer to my previous post "trace of a matrix"

M = $$\begin{pmatrix} 2 & -1 & 0 \\ -1 & 1 & 5 \\ 0 & 5 & 3\end{pmatrix}$$

from the following basis set:

$$\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{pmatrix}$$

$$\begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0\end{pmatrix}$$

$$\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1\end{pmatrix}$$

$$\begin{pmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0\end{pmatrix}$$

$$\begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{pmatrix}$$

$$\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{pmatrix}$$

Then what is the representation of M to this basis?

Homework Equations

The Attempt at a Solution

Homework Statement

M=[basis set]*B, where B is the rep. of M

Homework Equations

The Attempt at a Solution

There will be one (1x6) matrix for the coefficient's of M and (6x1) matrix for the basis set.

X= $$\begin{pmatrix} 2 \\ 1 \\ 3 \\ 0 \\ -1 \\ 5\end{pmatrix}$$

and 6 matrices for the basis set...

 

[lippyka]

B = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{pmatrix} Therefore, M=[basis set]*X.