Documentation / @interstellar-tools/equations / det3

Function: det3()

function det3(A: Matrix3x3Type): number;

Defined in: helpers/det-3.ts:52

Compute the determinant of a 3×3 matrix (row-major).

For:

$$\mathbf{A}=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$$

This returns:

$$det(\mathbf{A})=a(ei-fh)-b(di-fg)+c(dh-eg)$$

Notes:

• Matrices are treated as row-major: A[row][col].
• For a proper rotation matrix / DCM, det(A) ≈ +1.
• A determinant of 0 indicates the matrix is singular (non-invertible).

Parameters

Parameter	Type	Description
A	Matrix3x3Type	3×3 matrix (row-major).

Returns

number

Determinant det(A).

Examples

const I: Matrix3x3Type = [
  [1, 0, 0],
  [0, 1, 0],
  [0, 0, 1]
];

det3(I); // 1

const A: Matrix3x3Type = [
  [1, 2, 3],
  [0, 1, 4],
  [5, 6, 0]
];

det3(A); // 1