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Student[LinearAlgebra]

 Eigenvalues
 compute the eigenvalues of a square Matrix

 Calling Sequence Eigenvalues(A, options)

Parameters

 A - square Matrix; Matrix whose eigenvalues are required options - (optional) parameters; for a complete list, see LinearAlgebra[Eigenvalues]

Description

 • The Eigenvalues(A) command returns the eigenvalues of the square Matrix A, that is, the values t such that Determinant(A - t . Id(Dimension(A))) = 0.  The eigenvalues are returned in a (column) Vector.
 Note that eigenvalues are in general complex numbers.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{LinearAlgebra}]\right):$
 > $A≔⟨⟨1,3⟩|⟨3,-2⟩⟩$
 ${A}{≔}\left[\begin{array}{rr}{1}& {3}\\ {3}& {-}{2}\end{array}\right]$ (1)
 > $\mathrm{Eigenvalues}\left(A\right)$
 $\left[\begin{array}{c}{-}\frac{{1}}{{2}}{+}\frac{{3}}{{2}}{}\sqrt{{5}}\\ {-}\frac{{1}}{{2}}{-}\frac{{3}}{{2}}{}\sqrt{{5}}\end{array}\right]$ (2)
 > $B≔⟨⟨1,4,-2⟩|⟨-1,0,1⟩|⟨-1,2,1⟩⟩$
 ${B}{≔}\left[\begin{array}{rrr}{1}& {-}{1}& {-}{1}\\ {4}& {0}& {2}\\ {-}{2}& {1}& {1}\end{array}\right]$ (3)
 > $\mathrm{Eigenvalues}\left(B\right)$
 $\left[\begin{array}{c}{2}\\ {I}\\ {-}{I}\end{array}\right]$ (4)