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.