QR Factorization and Singular Value Decomposition
SVD and the Pseudoinverse • A-1=(VT)-1 W-1 U-1 = V W-1 UT • This fails when some w i are 0 – It’s supposed to fail – singular matrix – Happens when rectangular A is rank deficient • Pseudoinverse: if w i=0, set 1/w i to 0 (!) – “Closest” matrix to inverse – Defined for all (even non-square, singular, etc.) matrices
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