/sci/ - Science & Math

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

>>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.

The gamma function is a holomorphic continuation of the factorial and thus continuous in almost all of [math]\mathbb R[/math], so we can define a matrix function (so long as the eigenvalues aren't [math]-1,-2,...[/math] 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

>>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)

>>11730139