Determinants are explained here:
To find the determinant of:
| m00 | m01 | m02 | m03 |
| m10 | m11 | m12 | m13 |
| m20 | m21 | m22 | m23 |
| m30 | m31 | m32 | m33 |
note: I've started the index numbering from 0 instead of 1 so that the numering is more compatible with array indexing in programming languages.
The Laplace Expansion gives:
m00* |
|
-m01* |
|
+m02* |
|
-m03* |
|
These 3D minor determinants can then be expanded as in the 3D case.
So the value of the determinant for a 4×4 matrix is:
det = m03 * m12 * m21 * m30 - m02 * m13 * m21 * m30-
m03 * m11 * m22 * m30+m01 * m13 * m22 * m30+
m02 * m11 * m23 * m30-m01 * m12 * m23 * m30-
m03 * m12 * m20 * m31+m02 * m13 * m20 * m31+
m03 * m10 * m22 * m31-m00 * m13 * m22 * m31-
m02 * m10 * m23 * m31+m00 * m12 * m23 * m31+
m03 * m11 * m20 * m32-m01 * m13 * m20 * m32-
m03 * m10 * m21 * m32+m00 * m13 * m21 * m32+
m01 * m10 * m23 * m32-m00 * m11 * m23 * m32-
m02 * m11 * m20 * m33+m01 * m12 * m20 * m33+
m02 * m10 * m21 * m33-m00 * m12 * m21 * m33-
m01 * m10 * m22 * m33+m00 * m11 * m22 * m33
The following calculator allows you to calculate the determinant for a 4×4 matrix. Enter the values into the matrix and then press "calc det ->" to display the result:
// assumes matrix indices start from 0 (0,1,2 and 3)
public double determinant() {
double value;
value =
m03 * m12 * m21 * m30-m02 * m13 * m21 * m30-m03 * m11 * m22 * m30+m01 * m13 * m22 * m30+
m02 * m11 * m23 * m30-m01 * m12 * m23 * m30-m03 * m12 * m20 * m31+m02 * m13 * m20 * m31+
m03 * m10 * m22 * m31-m00 * m13 * m22 * m31-m02 * m10 * m23 * m31+m00 * m12 * m23 * m31+
m03 * m11 * m20 * m32-m01 * m13 * m20 * m32-m03 * m10 * m21 * m32+m00 * m13 * m21 * m32+
m01 * m10 * m23 * m32-m00 * m11 * m23 * m32-m02 * m11 * m20 * m33+m01 * m12 * m20 * m33+
m02 * m10 * m21 * m33-m00 * m12 * m21 * m33-m01 * m10 * m22 * m33+m00 * m11 * m22 * m33;
return value;
}
|
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.
