「逆行列」を編集中 (節単位)

== 3x3行列の場合 ==
:<math>
A^{-1} = \frac{1}{\text{det}(A)} \begin{bmatrix}
(a_{11}a_{22} - a_{12}a_{21}) & (a_{02}a_{21} - a_{01}a_{22}) & (a_{01}a_{12} - a_{02}a_{11}) \\
(a_{12}a_{20} - a_{10}a_{22}) & (a_{00}a_{22} - a_{02}a_{20}) & (a_{02}a_{10} - a_{00}a_{12}) \\
(a_{10}a_{21} - a_{11}a_{20}) & (a_{01}a_{20} - a_{00}a_{21}) & (a_{00}a_{11} - a_{01}a_{10})
\end{bmatrix}
</math>

C言語風に実装すると以下のような感じ。
<source lang="c">
bool inverseMatrix(float a[3][3], float inv[3][3]) {
    float det = a[0][0] * (a[1][1] * a[2][2] - a[2][1] * a[1][2]) 
              - a[0][1] * (a[1][0] * a[2][2] - a[1][2] * a[2][0]) 
              + a[0][2] * (a[1][0] * a[2][1] - a[1][1] * a[2][0]);

    if (det == 0) {
        printf("The matrix is singular and cannot be inverted.\n");
        return false;
    }

    float invdet = 1 / det;

    inv[0][0] =  (a[1][1] * a[2][2] - a[2][1] * a[1][2]) * invdet;
    inv[0][1] = -(a[0][1] * a[2][2] - a[0][2] * a[2][1]) * invdet;
    inv[0][2] =  (a[0][1] * a[1][2] - a[0][2] * a[1][1]) * invdet;

    inv[1][0] = -(a[1][0] * a[2][2] - a[1][2] * a[2][0]) * invdet;
    inv[1][1] =  (a[0][0] * a[2][2] - a[0][2] * a[2][0]) * invdet;
    inv[1][2] = -(a[0][0] * a[1][2] - a[1][0] * a[0][2]) * invdet;

    inv[2][0] =  (a[1][0] * a[2][1] - a[2][0] * a[1][1]) * invdet;
    inv[2][1] = -(a[0][0] * a[2][1] - a[2][0] * a[0][1]) * invdet;
    inv[2][2] =  (a[0][0] * a[1][1] - a[1][0] * a[0][1]) * invdet;

    return true;
}
</source>