condition number of a matrix

srobbert
77 ●1 ●3 ●7

5426 ●4 ●44 ●121

I am a novice Sage user, trying to get my Linear Algebra students to use Sage, too. One part of a problem I have assigned in the past asks a student to find the condition number of a matrix. In Maple, the command is just ConditionNumber(A), where A is a defined matrix. Is there a similar command in Sage?

Thanks for any help!

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answered 8 years ago

mforets
1413 ●9 ●27 ●44 http://marcelo-forets.fr/

Yes, check the method condition, as in:

A = random_matrix(RDF, 4)
A.condition(p=2) # produces the 2-norm (spectral norm) condition number 
15.7271056154     

sv = A.singular_values(); 
max(sv)/min(sv) # to check
15.7271056154

Type A.condition? for further examples.

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I assume this method only exists for matrices over "inexact rings", correct?

kcrisman ( 8 years ago )

@kcrisman that's accurate: both in RDF and CDF it exists, but not in ZZ, RR, QQ.

mforets ( 8 years ago )

Thanks! This helps--also with the random_matrix command that I didn't ask about!

Best to you!

srobbert ( 8 years ago )

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Last updated: Feb 09 '17

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