On this page we number the matrix elements with two index numbers the first represents the column, the second the row. The index numbers start at 0 as follows:
| m00 | m10 | m20 |
| m01 | m11 | m21 |
| m02 | m12 | m22 |
Other notation conventions are explained on this page.
The invese of a 3x3 matrix is:
| [M]-1 = 1/det[M] * |
|
where:
det = m00*m11*m22 + m01*m12*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 - m02*m11*m20
The above program is valid for a general 3×3 matrix which will work in all circumstances but when the matrix is being used to represent a rotation (as described on this page) then the matrix carries a lot of redundant information. So if we want to speed up the code on this page then, for this case only, we can take advantage of this redundant information. To invert a pure rotation then we just take the transpose of the 3x3 part of the matrix.
The following calculator allows you to calculate the inverse for a 3x3 matrix. Enter the values into the matrix and then press "calc inverse " to display the result:
public void inverse() {
double det = m00*m11*m22 + m01*m12*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 - m02*m11*m20;
m00 = (m11*m22 - m12*m21)/det;
m01 = (m02*m21 - m01*m22)/det;
m02 = (m01*m12 - m02*m11)/det;
m10 = (m12*m20 - m10*m22)/det;
m11 = (m00*m22 - m02*m20)/det;
m12 = (m02*m10 - m00*m12)/det;
m20 = (m10*m21 - m11*m20)/det;
m21 = (m01*m20 - m00*m21)/det;
m22 = (m00*m11 - m01*m10)/det;
}
|
metadata block |
|
| see also: |
|
| Correspondence about this page |
|
|
Book Shop - Further reading. Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them. |
|
|
Terminology and Notation Specific to this page here: |
|
This site may have errors. Don't use for critical systems.
Copyright (c) 1998-2023 Martin John Baker - All rights reserved - privacy policy.
