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Transformation matricies watch

1. I'm stuck!

What transformation would it be for this:
1/sqrt2 1/sqrt2
1/sqrt2 -1/sqrt2

How do i do it?
2. (Original post by xAres)
I'm stuck!

What transformation would it be for this:
1/sqrt2 1/sqrt2
1/sqrt2 -1/sqrt2

How do i do it?
What does it map and to?

Think about it geometrically and draw a picture.
3. (Original post by atsruser)
What does it map and to?

Think about it geometrically and draw a picture.
I and J?
4. (Original post by xAres)
I and J?
The unit vectors along the x and y axes i.e. and .

The columns of your matrix are the images of these vectors under matrix multiplication (check this). If you figure out what these vectors are mapped to, then you can figure out what anything is mapped to, since a general vector is:

and:

5. 0Its a reflection in the line y = (1/8)pi. If you're doing OCR A level it son p4 of the formula booklet.
6. (Original post by xAres)
I'm stuck!

What transformation would it be for this:
1/sqrt2 1/sqrt2
1/sqrt2 -1/sqrt2

How do i do it?
think about it and what a rotation matrix in your formula sheet looks like

alternatively see where it maps the four points
(1,0) (0,1) (-1,0) and (0,-1)
7. (Original post by natninja)
think about it and what a rotation matrix in your formula sheet looks like

alternatively see where it maps the four points
(1,0) (0,1) (-1,0) and (0,-1)
It makes sense now! Thanks!
8. (Original post by atsruser)
The unit vectors along the x and y axes i.e. and .

The columns of your matrix are the images of these vectors under matrix multiplication (check this). If you figure out what these vectors are mapped to, then you can figure out what anything is mapped to, since a general vector is:

and:

I get it now! I and J are just the identity matrix?

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