Matrix Function - Check Understanding

[Poetria]

Homework Statement

I have computed the matrix (it's ok):

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

The question is: what does this matrix do?

Relevant Equations

To figure it out, I have sketched two vectors:
[2,3] and the other - after transformation: [3,-2]

I would say that what this matrix does is rotate e.g. a vector by $\pi/2$ clockwise. Am I right?
I would like to check my understanding.

 

[FactChecker]

First, you have a mistake in the result for [2,3]. You need to correct that. Then take a general point, (x,y), in the $R^2$ plane and multiply it by the matrix. That will tell you where it ends up.

 

[Poetria]

First, you have a mistake in the result for [2,3]. You need to correct that. Then take a general point, (x,y), in the $R^2$ plane and multiply it by the matrix. That will tell you where it ends up.

Right, I have corrected it. :(

 

[FactChecker]

Right, I have corrected it. :(

I agree with your statements.

 

[Poetria]

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

 

[Poetria]

Great. :) Thank you so much. :)

 

[PeroK]

Homework Statement:: I have computed the matrix (it's ok):

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

The question is: what does this matrix do?
Relevant Equations:: To figure it out, I have sketched two vectors:
[2,3] and the other - after transformation: [3,-2]

I would say that what this matrix does is rotate e.g. a vector by $\pi/2$ clockwise. Am I right?
I would like to check my understanding.

You can look up the rotation matrix here:

https://en.wikipedia.org/wiki/Rotation_matrix

In your case, you are looking for $\cos \theta = 0$ and $\sin \theta = -1$. This is satisfied by $\theta = -\frac \pi 2$

 

[Poetria]

Many thanks. :)

You can look up the rotation matrix here:

https://en.wikipedia.org/wiki/Rotation_matrix

In your case, you are looking for $\cos \theta = 0$ and $\sin \theta = -1$. This is satisfied by $\theta = -\frac \pi 2$