# Getting a matrix

1. Jan 16, 2014

### Jhenrique

Given a vector r = (x, y, z) is possible to make some manipulation for get the matrix:
$$\begin{bmatrix} 0 & z & -y\\ -z & 0 & x\\ y & -x & 0\\ \end{bmatrix}$$
and this matrix too:
$$\begin{bmatrix} x & 0 & 0\\ 0 & y & 0\\ 0 & 0 & z\\ \end{bmatrix}$$
?

2. Jan 16, 2014

### Office_Shredder

Staff Emeritus
What do you mean by "manipulation"? You just wrote those matrices down, you now have them to do whatever you want with them. Are you asking whether the map
$$(x,y,z) \mapsto \left( \begin{array}{ccc} 0 & z & -y\\ -z & 0 & x\\ y & -x & 0 \end{array} \right)$$
is linear or something to that effect?

3. Jan 16, 2014

### Jhenrique

manipulation in the sense of add, subtract, multiply, divide... algebraic/matrix manipulation

4. Jan 25, 2014

### Jhenrique

I discovered how make the 1nd transformation!

Let [r] the notation for the first matrix of my post #1, it's is given by: $[\vec{r}] = \sqrt{\vec{r}\otimes \vec{r}-r^2 I}$

However, I still dont know how get the second matrix...

5. Jan 25, 2014

### AlephZero

A hint:

$\begin{pmatrix} 1 & 0 & 0 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} x \end{pmatrix}$

Then, use Kronecker products....

6. Jan 27, 2014

### Jhenrique

Give me an example