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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!
Nicolas

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Shanmukha Voggu
Shanmukha Voggu 2021-12-3
编辑：Shanmukha Voggu 2021-12-3

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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.

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That helped a lot, thanks!
Christine Tobler
Christine Tobler 2021-12-3
Hi, I just realized I got that wrong in the Answers post you were referring to: The complexity is actually
O(max(m, n) * min(m, n)^2)
That is, for a square n-by-n matrix the complexity of RANK is cubic in n.
Shanmukha Voggu
Shanmukha Voggu 2021-12-3
Thanks for the information, I edited my answer to show up right complexity
Thank you both for the clarification!
Walter Roberson
Walter Roberson 2021-12-6
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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