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# Eigenvalues

 Eigenvalues[m]gives a list of the eigenvalues of the square matrix . Eigenvalues[{m, a}]gives the generalized eigenvalues of with respect to . Eigenvalues[m, k]gives the first eigenvalues of . Eigenvalues[{m, a}, k]gives the first generalized eigenvalues.
• Eigenvalues finds numerical eigenvalues if 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 and 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 that are largest in absolute value.
• Eigenvalues[m, -k] gives the that are smallest in absolute value.
• The option settings and can be used to specify that explicit radicals should be generated for all cubics and quartics.
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Exact eigenvalues:
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Find approximate numerical eigenvalues:
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Find eigenvalues starting with 20-digit precision:
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Largest 5 eigenvalues:
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Multiple eigenvalues are listed multiple times:
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