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Jun. 13th, 2016 10:19 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
davvAnd now for something not as will-destroying:
I found out that there are "natural" matrix versions of a bunch of functions.
Suppose you have an entire function f(x) that inputs and outputs numbers. Being entire, it has a power series and that power series converges to f(x) for any value of x. Now, the trick is: since powers are defined for matrices as well, you can input a matrix into the power series. That generalizes f to a matrix-to-matrix function.
So you can take exponents of matrices, and also apply trig functions to them. That's a nice trick.
I found out that there are "natural" matrix versions of a bunch of functions.
Suppose you have an entire function f(x) that inputs and outputs numbers. Being entire, it has a power series and that power series converges to f(x) for any value of x. Now, the trick is: since powers are defined for matrices as well, you can input a matrix into the power series. That generalizes f to a matrix-to-matrix function.
So you can take exponents of matrices, and also apply trig functions to them. That's a nice trick.