anonymous
  • anonymous
let A be an orthogonal n x n matrix. show that ||Ax||=||A^(-1)x|| for any vector x in Rn
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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.
anonymous
  • anonymous
a sub(m,n) notation*
anonymous
  • anonymous
does that make sense?

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anonymous
  • anonymous
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.
anonymous
  • anonymous
haha, ok, good luck!!!
anonymous
  • anonymous
ok thanks again :)

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