Characteristic equation

{
  "id": "MLC-T-MET-004256",
  "term": "Characteristic equation",
  "field": "Meteorology and atmospheric science",
  "definition": "An algebraic equation derived from a system of linear differential equations or a matrix, whose roots determine the behavior or stability of the system. In atmospheric dynamics, it is used to find the eigenvalues of linearized equations, which represent growth rates or frequencies of atmospheric waves and instabilities. For example, the characteristic equation for a simple harmonic oscillator is mλ² + cλ + k = 0.",
  "see_also": [
    "characteristic-value problem"
  ],
  "url": "https://mlchart.com/terminology/meteorology/characteristic-equation/"
}