Is there a standard equation for a 4 by 4 inverse?

[HF08]

Inquiry:

Is there a standard equation for a 4 by 4 inverse? I know that one exists for 3 by 3, 2 by 2, but I cannot find one in my text nor in my searches online. I know I could find one by using the Jordan-Gaussian Method. But, I would be more comfortable with knowing a 4 by 4 general method/equation. I plan on doing a lot of inverses for a 4 by 4.

If you know of any resources, please help me. Also, if I should find this on my own by scratch, please help me.

Thank You,
HF08

 

[Dick]

Yes, you should probably create an explicit formula on your own. You don't find it listed just because it's lengthy to write down. But it should be an obvious extension of the lower dimensional cases. It's a matrix of the determinants of the minors of the nxn matrix divided by the determinant of the whole matrix.

 

[HF08]

Thanks

Yes, you should probably create an explicit formula on your own. You don't find it listed just because it's lengthy to write down. But it should be an obvious extension of the lower dimensional cases. It's a matrix of the determinants of the minors of the nxn matrix divided by the determinant of the whole matrix.

Can you please provide some links to the n = 2 and n = 3 cases please? After that, I'll do the rest on my own. Thanks.

HFO8

 

[Dick]

Look at the general analytic solution here http://en.wikipedia.org/wiki/Invertible_matrix#Analytic_solution

This a very inefficient way to actually do the inversion for large matrices, but if you work it through you can write down a lengthy 'formula'.