Matrix SVD Node

The Matrix SVD node computes the 3D singular value decomposition of the input matrix. The SVD describes the matrix in terms of a left and a right transformation U and V with a diagonal scaling matrix `S inbetween.

M = U * S * transpose(V)

Only the 3x3 part of the input matrix M is used, the translation part (4th column vector) is not used. The matrix does not have to be a pure (affine) transformation, any input matrix can be decomposed.

The output matrices U and V consist only of rotations and reflections (+1 or -1 scaling). If the input matrix M has a positive determinant then U and V are pure rotations. The scaling matrix S is described only by the diagonal vector.

入力

Matrix

The matrix to decompose.

出力

U

Left-hand transform.

S

Singular values.

V

Right-hand transform.