Eigenvalues
 Usage
• 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.
Notes
• 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. • New in Version 1; modified in 5. • Advanced Documentation.
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