Question

let A be an orthogonal n x n matrix. show that ||Ax||=||A^(-1)x|| for any vector x in Rn

Answer 1

so for Px = P^-1x...
[0,1; -1,0]x = [0,-1; 1,0}x
each system row reduces to {1,0; 1,0}....
to prove for any vector in r2, I would use the a sub(subm,n) notation...that is the most simple example that I can give...the column vectors form an orthonormal set and because it is a square matrix, its inverse is also equal to its transpose.

Answer 2

a sub(m,n) notation*

Answer 3

does that make sense?

Answer 4

Yeah dude I'm trying it right now, thanks I really appreciate it...might take awhile though lol can't concentrate everyone at my house is really extremely loud.

Answer 5

haha, ok, good luck!!!

Answer 6

ok thanks again :)