Game Development Reference
In-Depth Information
We find the determinant of a 3×3 matrix by first expanding the matrix by minors, and
then resolving the determinants of the 2×2 minors. Here's how you expand a 3×3 matrix
by minors:
Here's how this all looks in code:
inline float Matrix3x3::det(void)
{
return e11*e22*e33 -
e11*e32*e23 +
e21*e32*e13 -
e21*e12*e33 +
e31*e12*e23 -
e31*e22*e13;
}
Transpose
The method Transpose transposes the matrix by swapping rows with columns—that
is, the elements in the first row become the elements in the first column and so on for
the second and third rows and columns. The following relations are true for transpose
operations:
( M t ) t = M
(s M ) t = s ( M t )
( M N ) t = N t M t
( M + N ) t = M t + N t
det[ M t ] = det[ M ]
Here M and N are matrices, t is the transpose operator, and s is a scalar.
Here's the Transpose method for our Matrix3x3 class:
inline Matrix3x3 Matrix3x3::Transpose(void)
{
return Matrix3x3(e11,e21,e31,e12,e22,e32,e13,e23,e33);
}
Inverse
The method Inverse computes the inverse matrix such that the following relation is
satisfied:
M M −1 = M −1 M = I
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