Debug Info:
{
  "title": "Eigenvalue",
  "symbol": "λ",
  "definition": "An eigenvalue is a scalar associated with a linear system of equations that scales an eigenvector of a linear transformation.",
  "usage": "Used in studying dynamic systems, quantum mechanics, and data reduction techniques like Principal Component Analysis.",
  "examples": [
    {
      "description": "Eigenvalue equation",
      "latex": "A\\mathbf{v} = \\lambda\\mathbf{v}"
    },
    {
      "description": "Characteristic polynomial",
      "latex": "\\det(A - \\lambda I) = 0"
    }
  ],
  "tags": [
    "linear algebra",
    "matrices",
    "differential equations"
  ],
  "relatedConcepts": [
    "eigenvector",
    "diagonalization",
    "spectral theorem"
  ]
}

Eigenvalue

Symbol

λ

Definition

An eigenvalue is a scalar associated with a linear system of equations that scales an eigenvector of a linear transformation.

Usage

Used in studying dynamic systems, quantum mechanics, and data reduction techniques like Principal Component Analysis.

Examples

Tags

Related Concepts