Can anyone help me with this question:

Find a 3 by 3 orthogonal matrix which has 5/13 as its (2,2)-element..

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- April 9th 2009, 07:46 PMyakuutOrthogonal Matrix
Can anyone help me with this question:

Find a 3 by 3 orthogonal matrix which has 5/13 as its (2,2)-element.. - April 10th 2009, 12:31 AMOpalg
- April 10th 2009, 02:39 AMShowcase_22
I know I didn't post this question but I haven't got a clue how to do it either. (Crying)

After reading your post, here's what I tried:

Therefore I just need to arrange and in the matrix so that each vector is linearly independent from the other ones. I got this:

? - April 10th 2009, 03:21 AMOpalg
is fine for the middle column, but the other two columns are not orthogonal to it. You could for example use for one of them. Can you see a vector (hint: without any fractions in its entries) that is orthogonal to both of these?

Just to emphasise the point: linear independence is not enough, the columns must be orthogonal to each other. - April 10th 2009, 03:45 AMShowcase_22
- April 10th 2009, 04:04 AMOpalg
- April 10th 2009, 04:26 AMShowcase_22
YAY! (Cool)

Quote:

No, because those columns are not orthogonal. The scalar product of and is . You need exactly one coordinate to have a negative sign, so as to make the scalar product .

Thanks Opalg.