Documentation / @interstellar-tools/equations / transpose3

Function: transpose3()

function transpose3(A: Matrix3x3Type): Matrix3x3Type;

Defined in: helpers/transpose-3.ts:51

Transpose a 3×3 matrix (row-major).

For a matrix:

$$\mathbf{A}=\left[\begin{array}{ccc}{a}_{00}& a_{01}& a_{02}\\ a_{10}& a_{11}& a_{12}\\ a_{20}& a_{21}& a_{22}\end{array}\right]$$

the transpose is:

$${\mathbf{A}}^{\mathsf{T}}=\left[\begin{array}{ccc}{a}_{00}& a_{10}& a_{20}\\ a_{01}& a_{11}& a_{21}\\ a_{02}& a_{12}& a_{22}\end{array}\right]$$

Notes:

• Matrices are treated as row-major: A[row][col].
• For rotation matrices / DCMs, the transpose is also the inverse: ${\mathbf{R}}^{-1}={\mathbf{R}}^{\mathsf{T}}$.

Parameters

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

Returns

Matrix3x3Type

Transposed matrix Aᵀ (row-major).

Example

const A: Matrix3x3Type = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
];

const AT = transpose3(A);
// [
//   [1, 4, 7],
//   [2, 5, 8],
//   [3, 6, 9]
// ]