Question

1. (25 points) (hand solution) Find the Singular Value Decomposition (SVD) of A. Use the reduced version if the situation allows it 42 0 1 0 2 2 when producing the SVD. order the values such that σ1-σ2 On

Answer 1

0 Given that Find the singula value Deiomposi tion Lsv) Use the でeduced.vession £ he situ ation allows it. AAT 6 d 2 从4 and ATA 2 υάν aneoskhoma ma. velto of A ATA ATA

9 are eigen values. 9 k i) i> e'zen vetos 久ㄐ

2 obviousS So osthoaonaJ 5 ㄒ =0ノ4,9 e,-gen values.

ㄩ elgen vec tors ane. (using same talculation 5 They ane osthogemal,os thonosmad vectoss 51315 3/S

Note that H and. 9 ae nonmeus efgen values of both AAT and ATA £ is diagonal mat six non-3eno eigen valu es O 3O since Fisst tuo diagonai entires (singulah column . So 見 2. 3

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