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Matrix 2-norm Condition number

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Ammar Taha
Ammar Taha on 5 Jul 2020
Commented: Ammar Taha on 5 Jul 2020
I wanted to compare the result of the fucntion [cond();] which retrun the matrix 2-norm condition number as a ratio between the largest and the smallest singular value using the [isequal();] function with the result "segma" matrix of the SVD out of [svd();] fucntion as:
A = [1 2 5;4 8 7;8 9 5]; % example
[u,s,v] = svd(A);
c_num = cond(A);
sing_ratio = s(1,1)/s(end,end);
isequal(c_num, sing_ratio);
and the reslut was [0] although they are the same, and sadly this isn't the first tine that the equal function fails with me and don't know the reason.

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Matt J
Matt J on 5 Jul 2020
Edited: Matt J on 5 Jul 2020
sadly this isn't the first tine that the equal function fails with me and don't know the reason.
The isequal() function didn't fail. The two results are different ... just not by very much:
>> percent_difference=abs(c_num - sing_ratio)./c_num*100,
percent_difference =
2.4864e-14
If you want to know how cond() is computed, you can just read it:
>> type cond.m

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Ammar Taha
Ammar Taha on 5 Jul 2020
Thanks very much, I didn't give an attention to the infinitesimally small difference between them, but I got it when adjusted the format to be long.

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