Hi,

 

What are ultra-, super-, and sub-diagonal matrices?

 

Thanks

Silvia

The only Google results on it is you asking this question. So you probably should give us some context to actually help you answer your question. That is, cite the work where the terms are used, please.

The only seemingly relevant concept that was on Google was super matrices. http://en.wikipedia.org/wiki/Supermatrix

This seems close, but it's not the matrix itself that's subdiagonal.

http://en.wikipedia.org/wiki/Diagonal#Matrices

I guess the bottom left 4 elements of a 5 by 5 matrix could be described as a subdiagonal matrix, but I'm not sure the term would be useful.

My guess would be that the OP is referring to a band matrix where there are terms one or both sides of the main diagonal so the 'diagonal' is more than one term wide.

 

Such matrices are obtained in the solution of certain engineering problems by numerical methods.

 

http://en.wikipedia.org/wiki/Band_matrix

 

https://www.google.co.uk/search?hl=en-GB&source=hp&q=bnaded+matrix&gbv=2&oq=bnaded+matrix&gs_l=heirloom-hp.3..0i13l7j0i13i30l3.1407.3922.0.4079.13.13.0.0.0.0.218.1673.1j11j1.13.0.msedr...0...1ac.1.34.heirloom-hp..0.13.1673.If1_caZx51c

Edited March 22, 201510 yr by studiot

My guess would be that the OP is referring to a band matrix where there are terms one or both sides of the main diagonal so the 'diagonal' is more than one term wide.

 

Such matrices are obtained in the solution of certain engineering problems by numerical methods.

 

http://en.wikipedia.org/wiki/Band_matrix

 

https://www.google.co.uk/search?hl=en-GB&source=hp&q=bnaded+matrix&gbv=2&oq=bnaded+matrix&gs_l=heirloom-hp.3..0i13l7j0i13i30l3.1407.3922.0.4079.13.13.0.0.0.0.218.1673.1j11j1.13.0.msedr...0...1ac.1.34.heirloom-hp..0.13.1673.If1_caZx51c

Sure. I've done a ton of these numerical methods, and I agree the nomenclature is close, but not exactly what the OP was asking. That's why hopefully he comes back with some context.

http://mathworld.wolfram.com/Superdiagonal.html

http://mathworld.wolfram.com/Subdiagonal.html

http://mathworld.wolfram.com/JordanBlock.html

 

Ultradiagonal I could not find.

 

 

 

The only seemingly relevant concept that was on Google was super matrices. http://en.wikipedia.org/wiki/Supermatrix

I do not think super matrices are what Sarkuzi has in mind here. Superdiagonal I think notion they are looking for. (No idea why though)

Edited March 23, 201510 yr by ajb