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Let u be a unitary matrix in M2(ℝ).
Prove that if {b1, b2} is an orthonormal basis of ℝ2, then u(b2) is determined up to a negative sign by u(b1).
Can anyone provide some intuition that will help me understand the question (don't really understand it)? Any tips/hints appreciated.
Thanks.
Prove that if {b1, b2} is an orthonormal basis of ℝ2, then u(b2) is determined up to a negative sign by u(b1).
Can anyone provide some intuition that will help me understand the question (don't really understand it)? Any tips/hints appreciated.
Thanks.