MPINVERT: MoorePenrose Inverse of a Matrix

10272015, 06:57 PM
(This post was last modified: 10272015 07:01 PM by Han.)
Post: #7




RE: MPINVERT: MoorePenrose Inverse of a Matrix
(02062015 08:40 PM)salvomic Wrote: Hi Han, The vector of "real" values is a list of the singular values (i.e. the diagonal entries of \( \Sigma \). Quote:Those values are U, ∑, V and ∑ is the diagonal (√10, 0). Is it right? Yes. The help has been updated to correct the ordering of the output so that now it does in fact return \( \{ U, \Sigma, V \} \). Quote:And therefore, how can we operate to get ∑, A+ and so on? The pseudo inverse is \( V \Sigma^{1} U^{H} \) where \( U^H \) is the Hermitian (conjugate transpose for complex matrices, or just transpose for realvalued matriced) and \( \Sigma^{1} \) is simply the the transpose of \( \Sigma \) with the diagonal entry \( s_i \) replaced by \( \frac{1}{s_i} \). For values of \( s_i \) that are very small, (i.e. 0), then \( s_i \) is simply replaced by 0. Quote:Another thing: in that case Prime apparently give a vector with 3 elements (matrix, vector, matrix): there is a simple way to extract one of them, i.e. to make ration approximation (with QPI)? Please, help. You can use mat2list, and QPI accepts lists as input. Currently, the SVD() command is not as robust. I recommend using: http://hpmuseum.org/forum/thread4976.html I have updated the program to also include pinv() for pseudoinverse as well as pivoted QR factorization. This article has a decent interpretation of the SVD (though nowhere complete, however): http://robotics.caltech.edu/~jwb/courses...pseudo.pdf Graph 3D  QPI  SolveSys 

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Messages In This Thread 
MPINVERT: MoorePenrose Inverse of a Matrix  Eddie W. Shore  08292014, 09:30 PM
RE: MPINVERT: MoorePenrose Inverse of a Matrix  Namir  09012014, 09:11 PM
RE: MPINVERT: MoorePenrose Inverse of a Matrix  Han  02062015, 07:48 PM
RE: MPINVERT: MoorePenrose Inverse of a Matrix  salvomic  02062015, 03:09 PM
RE: MPINVERT: MoorePenrose Inverse of a Matrix  Han  02062015, 07:38 PM
RE: MPINVERT: MoorePenrose Inverse of a Matrix  salvomic  02062015, 08:40 PM
RE: MPINVERT: MoorePenrose Inverse of a Matrix  Han  10272015 06:57 PM
RE: MPINVERT: MoorePenrose Inverse of a Matrix  salvomic  10282015, 09:02 AM

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