condition number of a matrix

asked 2017-02-09 20:26:31 +0200

srobbert
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updated 2017-07-31 21:14:55 +0200

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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 2017-02-09 20:54:05 +0200

mforets
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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 ( 2017-02-09 22:28:51 +0200 )edit

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

mforets ( 2017-02-09 22:39:22 +0200 )edit

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

Best to you!

srobbert ( 2017-02-10 00:03:18 +0200 )edit

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Asked: 2017-02-09 20:26:31 +0200

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Last updated: Feb 09 '17

condition number of a matrix edit