Anyone have any experience with putting a matrix through a linear equation? Drowning computer science major here. Googling extensively isn't getting me anywhere. Any help would be greatly appreciated! (:
>>7711524
It's been a while but just input the matrix into the function and keep doing the operations until you have a final matrix.
It's tedious, but not difficult.
>>7711526
Do you mean first taking the matrix ^3, minus the matrix multiplied by 3 and ^2, etc? Before I was just taking each number of the matrix and putting it through the equation.
>>7711524
If the point of that exercise is finding nth powers of square matrices easily you should look up eigenvalues/vectors and diagonalization of matrices. Otherwise you can just do it the slow way, which in this case may be faster.
>>7711524
If you've learned about diagonalization, this is helpful.
>>7711524
>linear equation
What. Those are polynomials.
Anyway fun fact, the characteristic poly of A is x^2-x-8 so g(A)=0
https://en.wikipedia.org/wiki/Cayley%E2%80%93Hamilton_theorem
In general you can use the Cayley Hamilton Theorem to cut down on computations when generating powers of matrices
eg A^2=A+8I so thats pretty easy to work out
>>7711661
>Linear combination of matrices
>Not a linear equation
Fuck right off with your semantics
>>7711666
Not the guy you responded to, but that's the definition. No archaic meaning, just recognized and accepted definition.
>>7711666
If you see "^" it's not linear. Unless someone tries to look fancy doing ^0 or ^1.
Any variable squared - it's not linear.
And don't try to redefine things. It's like you tried to say addition is division, and cursed semantics if someone corrected you.
Polynomials of degree greater than 1 are not linear.
>>7711530
Sorry I couldn't reply before sperglord autists got here.
Yes, just input the entire matrix into the function and use the definitions for the matrix operations (they'll be in your book/notes most likely all in the same box).
>>7711689
if the matrix A is n*n, they're a linear combination over the vector subspace of N^(n*n) generated by the powers of A
>>7711700
Linear mathematics just refers to cases where superposition is applicable. It has nothing to do with powers.
>>7711700
...except in Boolean rings?
>>7711524
>those questions
I'm a CS major and even I find them silly
