More math (bah!)

I have a problem...

I have an nxn matrix A what I want to invert:

A^-1 * A = I
A^-1 * (A * A^T) = A^T
A^-1 * (L * L^T) = A^T
A^-1 * L = A^T * L^T^-1
A^-1 = A^T * L^T^-1 * L^-1

L is a lower triangular matrix such that (L * L^T) = (A * A^T). We get L with the use of Cholesky decompositio. It needs a symmetric, positive definite matrix to decompose; and multiplying a matrix with its own transpose always results with such.

Operation count:

A * A^T -> 1/2 * n^3 (we need only the half of the matrix)
cholesky decomposition: 1/6 * n^3
lower triangular inverting: 1/6 * n^3
A^T * L^T^-1 -> 1/2 * n^3
A^T * L^T^-1 * L^-1 -> 1/2 * n^3

total operation count: 11/6 * n^3 ~ 2 * n^3 -> BAAAAD! This is the problem!

To my knowledge this algorithm can be done with about 1 * n^3 operation counts, but I don't know how. Can anyone help?

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And another problem: how can I decompose an nxn matrix A into a symmetric matrix and any other component that is easily invertible, with few operations, and great stability?

 

And I will never ever ever ever ever write a song about a Frigo!

(I was going to sing "I freaking hate Frigo!" but that's not completely true, I just hate your maths.)

 

Frigo, If I would have known words and symbols you used, I maybe would have solved this problem.

 

... I think he's trying to slowly kill us.

 

No, Wolfsbanefurer, he only tries to establish new Austro-Hungarian Empire straightly on our heads.

 

Whatever he is doing, it's cunning and we couldn't guess what it is even in our wildest dreams.
He is deluding our minds with his strange and complex math while doing something unthinkable.

 

I have a question for you Frigo. This is one of my math problems. Ready?

Prove 7.

 

I did cryptography at uni and I have no fucking idea what you are talking about Frigo.

No u.

 

It's not crypto; it is just plain linear algebra, matrix inversion; with a "little" inaccuracy in the conventional notation; A^T means transposed A; A^-1 means inverted A.

But I have found the better algorithm I was talking about the end of my reply; I was misinformed, that algorithm used Strassen's algorithm, not Cholesky's.

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Did you learn RSA?

 

i loathe you.

 

Yes, yes I did learn RSA. I've still got my crypto text book actually.

 

11 = x + 4
- 4 - 4
7 = x
x = x
7 = 7

Right! Done with that... what's next?

 

Prove the existence of Void.

 

why don't you prove that y'all aren't losers?

 

Because we had not already studied how to prove it. :-(
Ot because this cannot be proved. :cry:

 

Good job, I think you just proved it. Dumb ass.

 

Thanks. :cry:

 

As a reward I present you with the Spoiled Cheese Whiz Of Mediocrity.

 

Because his mediocrity is only second to his inferiority?

 

Yes. I'm too bored to argument with you.