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Anonymous Fri 29 May 14:58:29 2020 No.11730139 View Reply Original Report

Quoted By: >>11730171 >>11730176 >>11730262

Do factorials of matrices exist?

Anonymous

Anonymous Fri 29 May 2020 15:08:20 No.11730171 Report

Quoted By:

>>11730139
not that i have heard of anything like it, but you could define it, probably only works with square matrixes tho

Anonymous

Anonymous Fri 29 May 2020 15:10:48 No.11730176 Report

Quoted By:

>>11730139
Only on a square matrix, and it wouldn't make sense unless each coefficient was the same. You could then derive that [2,2;2,2] factorial is just [2,2;2,2]x[1,1;1,1] = [4,4;4,4] and so on. Pardon my notation, I am a Matlab scumbag.

Anonymous

Anonymous Fri 29 May 2020 15:18:38 No.11730196 Report

Quoted By: >>11730200

The gamma function is a holomorphic continuation of the factorial and thus continuous in almost all of $\mathbb R$ , so we can define a matrix function (so long as the eigenvalues aren't $-1,-2,...$ or other negative integers) through a power series or the Jordan form as in: https://en.wikipedia.org/wiki/Matrix_function
See also: https://math.stackexchange.com/questions/1634488/how-could-we-define-the-factorial-of-a-matrix
And: >>>/sci/sqt

Anonymous

Anonymous Fri 29 May 2020 15:20:34 No.11730200 Report

Quoted By:

>>11730196 (Me)
ah, and of course this assumes a square matrix as other anons have pointed out. doesn't make a ton of sense if you can't compose the matrix with itself (as is the case for non-square matrices)

Anonymous

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Anonymous Fri 29 May 2020 15:46:59 No.11730262 Report

Quoted By:

>>11730139

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