(no subject)

[davv]

And 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.

Comments

[lhexa]

Yep! That particular trick is quite useful in quantum mechanics, where you can even work with infinite-dimensional matrices and converging power series thereof.