/// <summary>
/// Produces the determinant of a square matrix
/// </summary>
/// <param name="mat">The matrix</param>
/// <returns>The determinant of the matrix</returns>
public static T Determinant <T>(this T[,] mat)
{
MatrixDimensions d = mat.GetDimensions();
if (d.IsSquare())
{
switch (d.rows)
{
case 0:
throw new MatrixSizeException("A matrix cannot have no elements.");
case 1:
return(mat[0, 0]);
case 2:
return(mat[0, 0] * (dynamic)mat[1, 1] - mat[0, 1] * (dynamic)mat[1, 0]);
default:
T sum = mat[0, 0] * (dynamic)(mat.RemoveVector(VectorDirection.Row, 1).RemoveVector(VectorDirection.Column, 1).Determinant());
for (int i = 1; i < d.rows; i++)
{
if (i % 2 == 0)
{
sum += mat[0, i] * (dynamic)(mat.RemoveVector(VectorDirection.Row, 1).RemoveVector(VectorDirection.Column, i + 1).Determinant());
}
else
{
sum -= mat[0, i] * (dynamic)(mat.RemoveVector(VectorDirection.Row, 1).RemoveVector(VectorDirection.Column, i + 1).Determinant());
}
}
return(sum);
}
}
throw new IllegalOperationException("Only squre matricies have determinants.");
}
/// <summary>
/// Calculates the inverse of a matrix, if it has one
/// </summary>
/// <param name="matrix">The matrix</param>
/// <returns>The matrix's inverse</returns>
public static T[,] Inverse <T>(this T[,] matrix)
{
MatrixDimensions d = matrix.GetDimensions();
if (!d.IsSquare())
{
throw new MatrixSizeException("A non-square matrix cannot have an inverse.");
}
T[][,] aug = matrix.Augment(Matrix <T> .IdentityMatrix(d.cols)).RREF().Separate(d.cols, d.cols);
if (!aug[0].IsIdentity())
{
throw new IllegalOperationException("A matrix with no identity has no inverse.");
}
return(aug[1]);
}