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BUILT-IN MATHEMATICA SYMBOL
Eigenvalues
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[{m, a}, k]
gives the first k generalized eigenvalues.
Details and Options
- 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
are those 
for which 
for some non-zero eigenvector 
. - The generalized eigenvalues of
with respect to 
are those 
for which 
. - 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.
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