Example: barber
L.Vandenberghe ECE133A(Fall2018) 5.Orthogonalmatrices
Proof thesquareddistanceofb toanarbitrarypointAx inrange„A”is kAx bk2 = kA„x xˆ”+ Axˆ bk2 (wherexˆ = ATb) = kA„x xˆ”k2 + kAxˆ bk2 +2„x xˆ”TAT„Axˆ b” = kA„x xˆ”k2 + kAxˆ bk2 = kx xˆk2 + kAxˆ bk2 kAxˆ bk2 withequalityonlyifx = xˆ line3followsbecauseAT„Axˆ b”= xˆ ATb = 0 line4followsfromATA = I Orthogonalmatrices 5.18
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