Documentation / @interstellar-tools/equations / applyMatrix3

Function: applyMatrix3()

function applyMatrix3(
  M: Matrix3x3Type,
  v: Vector3DTupleType
): Vector3DTupleType;

Defined in: helpers/apply-matrix-3.ts:38

Apply a 3×3 matrix to a 3D vector (matrix–vector multiplication).

Computes:

$$\mathbf{y}=\mathbf{M}\mathbf{v}$$

With row-major indexing:

• M[row][col]
• v = [x, y, z]

This is commonly used for:

• Applying a direction cosine matrix (DCM) / rotation matrix to transform vectors between frames (e.g., inertial → body-fixed).
• Small 3D linear transforms in geometry and mapping pipelines.

Parameters

Parameter	Type	Description
M	Matrix3x3Type	3×3 matrix (row-major) (all finite).
v	Vector3DTupleType	3D vector [x, y, z] (all finite).

Returns

Vector3DTupleType

The transformed vector M * v as a 3D tuple.

Example

const M: Matrix3x3Type = [
  [1, 0, 0],
  [0, 0, -1],
  [0, 1, 0]
];

const v: Vector3DTupleType = [1, 2, 3];
const out = applyMatrix3(M, v);
// out === [1, -3, 2]