Difference between revisions of "Determinant of a matrix"
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{{Navigation|before=[[Minors and cofactors]]|overview=[[Matrices]]|next=[[Matrix inversion]]}} | {{Navigation|before=[[Minors and cofactors]]|overview=[[Matrices]]|next=[[Matrix inversion]]}} | ||
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| + | For 3-by-3 and smaller matrices there are simple formulas to compute the determinant. Useful to compute the determinant of larger matrices are the minors and cofactors which are explained in the first subarticle. Based on these an example formula to compute the determinant of a 4-by-4 matrix is presented afterwards. | ||
This article describes a formula to compute the determinant of a 4-by-4 matrix using [[Minors_and_cofactors|minors and cofactors]] of a matrix.<br/> | This article describes a formula to compute the determinant of a 4-by-4 matrix using [[Minors_and_cofactors|minors and cofactors]] of a matrix.<br/> | ||
Revision as of 13:31, 19 May 2014
| ← Back: Minors and cofactors | Overview: Matrices | Next: Matrix inversion → |
For 3-by-3 and smaller matrices there are simple formulas to compute the determinant. Useful to compute the determinant of larger matrices are the minors and cofactors which are explained in the first subarticle. Based on these an example formula to compute the determinant of a 4-by-4 matrix is presented afterwards.
This article describes a formula to compute the determinant of a 4-by-4 matrix using minors and cofactors of a matrix.
To compute the determinant of matrix 
first one row or column is choosen. The sum of the four corresponding values of the row or column multiplied by the related cofactors results in the determinant:
 Example: determinant of a 4-by-4 matrix
|
![\mathbf{A}_e =
\left[\begin{array}{cccc}
1 & 2 & 0 & 0\\
3 & 0 & 1 & 1\\
0 & 1 & 0 & 0\\
0 & 0 & 2 & 1
\end{array}\right]](/wiki/robotics/images/math/a/3/8/a386cb4eac26aca26ac89fd336061a0e.png)
it is useful to choose row 3 because it contains three zero values as factors:
