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FB_107959225-Regular Member
5-Regular Member
July 9, 2025
Question

Singular Value Decomposition

  • July 9, 2025
  • 3 replies
  • 707 views

Dear all?

 

I'd like to have some deeper / practical information on SVD function.

 

From theoretical lectures it seems to me that Singular Value Decomposition could me a useful tool to tackle ill-conditioned matrix in eigenvectors search for homogeneous linear system.

 

It appears also that SVD can solve a variety of problems; that does not help that much me as explanations are often at a too "high level".....

 

The material in MathCAD help is, sorry to say, in the same league: too abstract...I had also a look to the only one post on similar subject, and again sorry not so easy to be adapted to my problem (not so specialized by the way...)

 

Could you:

1) confirm me that what I've understood from theoretic is reasonably correct 

2) give a more workable example: for example the search for eigenvectors (linked to eigenvalues) for a linear system 4 equations in 4 unknowns (using the MathCAD SVD algorithm)? The best would be that the square matrix linked with the said system is ill-conditioned.....

 

Thank you very much in advance

3 replies

W
Werner_E25-Diamond I
25-Diamond I
July 9, 2025

Can't contribute much of my own concerning your question.

You sure have already seen the example in the help!? -> Example: SVD Matrix Factorization

The matrix used stems from a Quicksheet which was part of the help in good old legacy Mathcad.

I attach this Quicksheet in its original format and also converted to Prime 11, maybe it can be useful for you.

 

F
FB_107959225-Regular MemberAuthor
5-Regular Member
July 9, 2025

Thanks WERNER_E but not possible for me to read the attachmnets as I'm working (for the moment at least) only with PRIME 9.0....

W
Werner_E25-Diamond I
25-Diamond I
July 9, 2025

I noticed that you did not mention the version of Prime you are using. That's the reason why I also attached the original legacy version so you can convert it on your own using the version you are using. In case you did not install the converter when you installed Prime you can run the installer once again an add the converter.

Find attached a pdf print of the file. I fear it will not show much more information compared to the example given in the Prime help.

 

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
July 10, 2025

https://www.youtube.com/watch?v=mBcLRGuAFUk

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
July 10, 2025

Hi,

2) give a more workable example: for example the search for eigenvectors (linked to eigenvalues) for a linear system 4 equations in 4 unknowns (using the MathCAD SVD algorithm)? The best would be that the square matrix linked with the said system is ill-conditioned.

 

See enclosed file where SVD is linked to eigenvalues and eigenvectors of two matrices MTM and MMT.

Cheers

Terry

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