Skip to main content
L
LarryJ10-Marble
10-Marble
April 30, 2023
Solved

Schur and Jordan decompositions of a Matrix

  • April 30, 2023
  • 3 replies
  • 6133 views

 

Would be nice if Mathcad Prime included internal routine for the Schur and Jordan decompositions of a matrix.

Has anyone developed a Mathcad Prime routine to return the Schur and Jordan decompositions of a matrix?

 

Thanks for any help.

Best answer by LarryJ

Terry,

See attached - I think I cracked it.  I finally got Schur decomposition to work on matrix with a mix of real and pairs of complex conjugate eigenvalues with reduced iterations.  Also added routine to get eigenvectors from Schur decomposition. ðŸ˜Š

 

I think this should be considered an accepted solution. Do you agree?

 

Now need to work on a Mathcad version of the Jordan decomposition with repeated eigenvalues. 

It would be nice if Mathcad included efficient versions of the Schur and Jordan decomposition for eigenvalues and eigenvectors in their list of matrix functions.😩

 

I wanted to add ViadimirN and Werner_E to posting, but don't see how to do it.

 

Thanks all for your help😊

LarryJ

3 replies

V
24-Ruby III
VladimirN24-Ruby III
24-Ruby III
April 30, 2023

You can look at an old discussion here - "Jordansche Normalform of a matrix": https://community.ptc.com/t5/Mathcad/Jordansche-Normalform-of-a-matrix/td-p/81283

L
LarryJ10-MarbleAuthor
10-Marble
May 1, 2023

Thanks for the Link -- interesting discussion but I was looking for a mathcad algorithm that someone may have developed in the past.

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
April 30, 2023

Hi Larry,

Here is the Schur decomposition for real matrix and real eigenvalues, have not developed the complex number algorithm yet.

Following are two examples from different sources.

Capture.JPG

Capture2.JPG

Capture3.JPG

Cheers

Terry

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
May 1, 2023

Hi,

Realize the iterative solution often needs far less than 2 million iterations.

Here is a solution that defines the maximum number of iterations "n" and an accuracy in decimal places "d"

Capture.JPG

Capture2.JPG

Cheers

Terry

L
LarryJ10-MarbleAuthor
10-Marble
May 1, 2023

This is better solution -- will it work for complex matrix?

What is 

LarryJ_0-1682929661420.png

Thanks

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
May 8, 2023

Hi,

Jordan Decomposition.

3x3 file has commentary, 4x4 file just does the calculations.

L
LarryJ10-MarbleAuthor
10-Marble
May 8, 2023

Thanks for the contribution. I'll have to figure out how to program that process.

Terms & ConditionsCookie settingsAccessibility statement