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Student[LinearAlgebra]

 CharacteristicMatrix
 construct a characteristic Matrix

 Calling Sequence CharacteristicMatrix(A, t, options)

Parameters

 A - square Matrix t - name; variable options - (optional) parameters; for a complete list, see LinearAlgebra[CharacteristicMatrix]

Description

 • The CharacteristicMatrix(A, t) command constructs the characteristic Matrix $M=-t\mathrm{Id}+A$, where Id is the appropriately sized identity Matrix. The determinant of M, found by using $\mathrm{Determinant}\left(M\right)$, is the characteristic polynomial of A.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{LinearAlgebra}}\right):$
 > $A≔⟨⟨1,2,3⟩|⟨1,2,3⟩|⟨1,5,6⟩⟩$
 ${A}{≔}\left[\begin{array}{ccc}{1}& {1}& {1}\\ {2}& {2}& {5}\\ {3}& {3}& {6}\end{array}\right]$ (1)
 > $C≔\mathrm{CharacteristicMatrix}\left(A,t\right)$
 ${C}{≔}\left[\begin{array}{ccc}{t}{-}{1}& {-1}& {-1}\\ {-2}& {t}{-}{2}& {-5}\\ {-3}& {-3}& {t}{-}{6}\end{array}\right]$ (2)
 > $\mathrm{Determinant}\left(C\right)$
 ${{t}}^{{3}}{-}{9}{}{{t}}^{{2}}$ (3)
 > $\mathrm{CharacteristicPolynomial}\left(A,t\right)$
 ${{t}}^{{3}}{-}{9}{}{{t}}^{{2}}$ (4)