This example classifies three small complex-valued matrices for a discrete-time system. In everyday terms, it asks whether repeated application of a matrix makes a signal grow, stay on the edge of stability, or shrink away.
The matrices are diagonal, which keeps the example focused on the stability rule rather than on matrix algebra machinery.
For a diagonal matrix, the important values are already on the diagonal. Each diagonal entry is a complex number. The program computes the modulus, or distance from zero, of each complex number.
The largest modulus is called the spectral radius. A radius greater than 1 means repeated steps can grow, so the system is unstable. A radius equal to 1 is marginally stable. A radius below 1 is damped.
The output labels the three matrices as unstable, marginally stable, and damped. This makes the stability boundary visible: the difference between radius 1 and radius 2 is not just numerical; it changes the long-term behavior.
The trust gate verifies that every matrix is classified, every radius is derived from the matrix diagonal, every class follows from its radius, and a basic complex-number identity about product moduli holds. That last check protects the small complex arithmetic helper used by the example.
From the repository root:
node examples/complex_matrix_stability.js