DocumentationMathematicaBuilt-in FunctionsNew in Version 5.0Lists and Matrices
Eigenvalues[m] gives a list of the eigenvalues of the square matrix m.
Eigenvalues[m, a] gives the generalized eigenvalues of m with respect to a.
Eigenvalues[m, k] gives the first k eigenvalues of m.
Eigenvalues finds numerical eigenvalues if m contains approximate real or complex numbers.
Repeated eigenvalues appear with their appropriate multiplicity.
An matrix gives a list of exactly eigenvalues, not necessarily distinct.
If they are numeric, eigenvalues are sorted in order of decreasing absolute value.
The eigenvalues of a matrix m are those for which m . v == v for some non-zero eigenvector v.
The generalized eigenvalues of m with respect to a are those for which m . v == a . v.
When matrices m and a have a dimension- shared null space, then of their generalized eigenvalues will be Indeterminate.
Ordinary eigenvalues are always finite; generalized eigenvalues can be infinite.
For numeric eigenvalues, Eigenvalues[m, k] gives the k that are largest in absolute value.
Eigenvalues[m, -k] gives the k that are smallest in absolute value.
Eigenvalues[m, spec] is always equivalent to Take[Eigenvalues[m], spec].
The option settings Cubics->True and Quartics->True can be used to specify that explicit radicals should be generated for all cubics and quartics.
SparseArray objects can be used in Eigenvalues.
See Section 1.8.3 and Section 3.7.9.
See also: SingularValueList, CharacteristicPolynomial, Det, Tr.
New in Version 1; modified in 5.0.