rank() computation cost

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Nicolas Mira Gebauer
Nicolas Mira Gebauer on 30 Nov 2021
Commented: Walter Roberson on 6 Dec 2021
Hi, does anyone knows which is the computational cost of getting the rank of a matrix through the rank(M) command? (It would be extremelly usefull to have the order of the command using the Big O notation.
Thank you in advance!

Accepted Answer

Shanmukha Voggu
Shanmukha Voggu on 3 Dec 2021
Edited: Shanmukha Voggu on 3 Dec 2021
Hi Nicholas,
The Computational Complexity of the rank function is equal to svd function.
which is equal to O(max(m, n) * min(m, n)^2), where m and n are number of rows and columns of the matrix respectively
Refer this for more information.
Walter Roberson
Walter Roberson on 6 Dec 2021
I was wondering! max(m, n) *min(m, n) as was posted before is the same as m*n, and I couldn't figure out why someone would bother writing it the long way!

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