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October 18th, 2013, 11:05 AM   #1
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A reconciliation of Pseudoinverse

I want to this two :

A^- A A^- = A^-

(A^-A)^T = A^-A


A have this two is already:

A A- A = A
reconciliation :
A((A^T A)^- A^T A) = A ((A^T A)^-)(A^T A) = A

(A A-)= A A-
reconciliation :
(A A-) = ((A(A^T A)^- A^T))^T = (A-)^T A^T = (A^T)^T (A^T A)^-)^T A^T = A(A^T A)^- A^T
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