Let A be an orthogonal 2x2 matrix. Use the image of the unit circle to find the singular values of A.
Seems like it should be an easy question but I don't understand how to do it...help please!
Ok, so now we know what they are. Now, an orthogonal (real, of course...otherwise you'd call it unitary, right?) matrix is
of the form , or ,where we can (not must) take
Take for example the first kind, then , so the singular values are ... .
Of course, this follows at once from the fact that for orthogonal (real) matrices....