#### Archived

This topic is now archived and is closed to further replies.

# Inverse of a Matrix

This topic is 6959 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hey everyone. I need some help. I have forgotten how to inver a 4x4 matrix. I remember how to inver a 2x2 and a 3x3, but a 4x4 (or an NxN for that matter) uses a different algorithm. Any replies (relevant) will be greatly appreciated.

##### Share on other sites

Do you know how to do a Gauss-Jordan reduction on a matrix?

If so, in order to calculate the inverse of an n x n matrix you can simply create a new matrix with the n x 2n matrix with the right square being the matrix to be inverted and the left square being the n x n identity matrix, and perform a gaussian reduction on the matrix.

So if you want to invert:
[1 2 3]
[1 4 9]
[1 1 1]
create a matrix:
[1 2 3 1 0 0]
[1 4 9 0 1 0]
[1 1 1 0 0 1]
And perform the reduction and you''d get:
[1 0 0 -2.5 .5 3]
[0 1 0 4.0 -1 -3]
[0 0 1 -1.5 .5 1]

And the matrix
[-2.5 .5 3]
[4.0 -1 -3]
[-1.5 .5 1]
is the inverse.

##### Share on other sites
There''s source code for both Gaussian elimination and Cramer''s rule in this article from Intel:

AP-928 Streaming SIMD Extensions -Inverse of 4x4 Matrix

Oh, and don''t mind that it says SIMD Extensions, it shows how to do it with normal instructions as well.

• 10
• 13
• 52
• 11
• 15