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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] * |
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where:
det = m00*m11*m22 + m01*m12*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 - m02*m11*m20
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;
}
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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. |
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Can you help? Please send me any improvements to here. I would appreciate ideas to make the pages more useful including error correction, ideas for new pages, improvements to wording. It helps if you quote the full URL of the page. |
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Terminology and Notation Specific to this page here: |
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program I am working on a project which uses these principles, if you would like to help me with this you are welcome to join in, here: |
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