is there a very easy to code way of calculating the determinant using the inverse?

[Kuciwalker]

I've painstakingly debugged my code that brings a matrix into reduced echelon form, to calculate the inverse. The prospect of writing the recursive function for the determinant is not inviting. Isn't there some way of using the inverse to find the determinant?

[KrazyHorse]

a) the determinant of the inverse is the inverse of the determinant

b) instead of using a recursive function to calculate the determinant by minors, use the the even/odd permutation definition of determinant

c) write down the eigenvalue equation for the matrix, solve for the roots and multiply them together to get the determinant

[KrazyHorse]

The determinant is properly defined as:

the sum over all permutations sigma of (-1)^(sign of sigma) a1sigma(1)a2sigma(2)...ansigma(n)

[Ramo]

I've painstakingly debugged my code that brings a matrix into reduced echelon form, to calculate the inverse. The prospect of writing the recursive function for the determinant is not inviting. Isn't there some way of using the inverse to find the determinant?

Not unless its inverse is easy to calculate.

Easiest way would be this:

detA = e_q1...qnA₁^q1...A_n^qn

Edit: In case it's not clear, the summation over each qm is implied through repeated indices. And e_q1...qn gives 1 if q1..qn is an even permutation of 1...n, -1 if it's an odd permutation.

[Sava]

MATH DORK THREAD!@@!~!!@!!!!@111one!!11!!!

[KrazyHorse]

If you've written down the row-reduced echelon form of the matrix and this has non zero determinant (i.e. it's the unit matrix) then if you've kept track of the operations performed to get ther then the determinant is trivial to calculate...

[Kuciwalker]

Originally posted by KrazyHorse
If you've written down the row-reduced echelon form of the matrix and this has non zero determinant (i.e. it's the unit matrix) then if you've kept track of the operations performed to get ther then the determinant is trivial to calculate...

*looks at wikipedia*

Thanks! That's really, really easy to implement.

[KrazyHorse]

How big is this matrix?

[Asher]

Are you writing this in Fortran?

[Kuciwalker]

Originally posted by KrazyHorse
How big is this matrix?

Arbitrarily sized (= I hardcoded allocation of 100x100 ints assuming my instructor won't wan't to type 10,000 numbers in to check my program ).

And it's in C.

[KrazyHorse]

Won't it take forever to run anything larger than 20X20 or so?

[Kuciwalker]

Probably.

(The assignment is a linear algebra assignment, it's more my computer architecture class. It's more a "can you write in C, and can you do all this stuff while handling all sorts of crap user input and make it bug-free" sort of assignment.)

[KrazyHorse]

I think exact inversion runs in N^3 time. Can't remember.

[Kuciwalker]

My algorithm is N^3, I think.

[KrazyHorse]

approximate numerical inversion is much faster.