Ee1036cS10

Ee1036cS10 - QR Factorization (Projection Point-of View)...

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QR Factorization (Projection Point-of View) th d fl t Factorization Summary 3 3 2 2 33 22 2 3 1 3 ,, purpose metho df l ops comments Ax b n n CGE inv inv inaccurate Ax b n n LU inv not computed nn n n   3 3 1 3 2 26 2 5 1 2 53 2 , ;? , TT A Ax A b Choleski LS also used for PD Ax b m n QR n m used for LS mn n n n  EE103 SLIDES 6C (SEJ) 1 QR Factorization (Projection Point-of View) 2 a 11 /( ) an o r m a T T 0 T vu u v u u u v u v v u u      () T Iu uv EE103 SLIDES 6C (SEJ) 2
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def m A mnr a n kA n Rx A x    ,, () {| } 12 n lin comb a a a column space A  {} ( also called the range of A (" " ) _{ ,,, }_ ) EE103 SLIDES 6C (SEJ) 3 QR Factorization (an alternative and clearer geometric explanation) ,1 m uR u 2 , TT uu P uu and P I uu m m matrices  2 : T Note P P and P P "" Such matrices are called orthogonal projection matrices (..
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Ee1036cS10 - QR Factorization (Projection Point-of View)...

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