False correct 2 true explanation when p is orthogonal

  • University of Texas
  • EXAM 04
  • Test Prep
  • Lieutenant62
  • 8
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1.FALSEcorrect2.TRUEExplanation:WhenPis orthogonal andx=Py, thenQ(x) =xTAx= (Py)TA(Py)=yTPTA Py=yT(PTAP)y.But this will contain cross-product terms un-lessPTAPis adiagonalmatrix,i.e., unlessAis orthogonally diagonalized byP.
Consequently, the statement isFALSE.01210.0 points
Explanation:Whenv1,v2areorthonormaleigenvectorsofAcorresponding to respective eigenvaluesλ1andλ2, then the spectral decomposition ofAis given byA=λ1v1vT1+λ2v2vT,and the component determined byλ1isλ1v1vT1.
Version 047 – NewEXAM04 – gilbert – (53525)
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