Eig (General)

Shipping

matrix_eig

General (non-symmetric) eigen-decomposition with real+imag facade ports and unified complex arrays

Signature

Inputs

aSignal|Arrayrequired— A general (possibly non-symmetric) square 2-D matrix.

Outputs

eigenvalues_reVector— Real parts of the eigenvalues (legacy compat facade).
eigenvalues_imVector— Imaginary parts of the eigenvalues (legacy compat facade).
eigenvectors_reMatrix— Real parts of the eigenvectors (legacy compat facade).
eigenvectors_imMatrix— Imaginary parts of the eigenvectors (legacy compat facade).
eigenvaluesArray— Eigenvalues as a unified complex array (eps-collapses to real for a real spectrum).
eigenvectorsArray— Eigenvectors as a unified complex array.

Description

Eig (General) computes the eigen-decomposition of a general (not necessarily symmetric) square matrix via MKL LAPACK, where eigenvalues and eigenvectors may be complex even for a real input (a rotation matrix, for example, has complex-conjugate eigenvalues).

It exposes six output ports. Four legacy real ports — eigenvalues_re, eigenvalues_im, eigenvectors_re, eigenvectors_im — form a compatibility facade so previously-saved .cap wirings keep working. Two unified complex Array ports — eigenvalues and eigenvectors — carry the spectrum as single complex arrays and are the recommended modern outputs; they automatically eps-collapse to real when the spectrum is real. All outputs are dimensionless.

When you know the matrix is symmetric, prefer matrix_eigh: it is faster, guarantees real results, and returns an orthonormal basis.

Mathematics

A v_{i} = λ_{i} v_{i}, λ_{i}, v_{i} \in C

e.g. [01 - 1 0] \Rightarrow λ = \pm i, ∣ λ ∣ = 1

Examples

Complex eigenvalues of a rotation

The $9 0^{\circ}$ rotation $A = [01 - 1 0]$ has eigenvalues $\pm i$ . On this node the legacy eigenvalues_im port reads $\approx [- 1, + 1]$ , while the unified eigenvalues complex-array port reports two values each with magnitude $1$ .

Applications

Stability analysis of non-symmetric state matrices (eigenvalues in the complex plane).
Modal decomposition of general (damped, gyroscopic) dynamical systems.
Spectral analysis where complex conjugate pairs encode oscillatory modes.
Migrating older graphs that read separate real/imag eigen ports.

Neat

The four real re/im ports are a deliberate compatibility facade so old saved graphs never break, while #126's unified complex Array ports are the clean modern path.

The complex arrays eps-collapse to real automatically, so a genuinely real spectrum doesn't drag along a zero imaginary part downstream.

Known issues

For symmetric matrices this is slower and less accurate than matrix_eigh and may return tiny spurious imaginary parts — prefer eigh when symmetry holds.

Eigenvector scaling and phase are not unique for complex spectra, so vector columns may differ (by a unit-modulus factor) across runs.