Question

A matrix U in Rnxn is said to be orthogonal if UtU=I (U transpose*U=I). What are the possible values of determinant U?

Answer 1

isnt an orthogonal square matrix independant?

Answer 2

Yes, I'm pretty sure

Answer 3

and since all independent square matrixes are row equivalent to the Identity matrix; what is the determinant of the Identity matrix?

Answer 4

1

Answer 5

So would this imply that this only works for the identity matrix?

Answer 6

Or that it works for others, but their determinant will always be one?

Answer 7

no, this works for all independent square matrixes, since they all can be row reduced to equal the indentity matrix (which itself is orthogonal).

Answer 8

Okay, this makes sense.

Answer 9

Thank you!

Answer 10

youre welcome