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Student[LinearAlgebra]

 JordanForm
 reduce a Matrix to Jordan form

 Calling Sequence JordanForm(A, options)

Parameters

 A - Matrix options - (optional) parameters; for a complete list, see LinearAlgebra[JordanForm]

Description

 • The JordanForm(A) command returns the Jordan form J of Matrix A.
 The Jordan form J has Jordan block submatrices along its diagonal. The diagonal entries of these Jordan blocks are the eigenvalues of A (and also of J).
 The Jordan form is unique up to permutations of the Jordan blocks.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{LinearAlgebra}]\right):$
 > $A≔⟨⟨0,-2,-2,-2⟩|⟨-3,1,1,-3⟩|⟨1,-1,-1,1⟩|⟨2,2,2,4⟩⟩:$
 > $J≔\mathrm{JordanForm}\left(A\right)$
 ${J}{≔}\left[\begin{array}{rrrr}{0}& {1}& {0}& {0}\\ {0}& {0}& {0}& {0}\\ {0}& {0}& {2}& {0}\\ {0}& {0}& {0}& {2}\end{array}\right]$ (1)
 > $\mathrm{Eigenvalues}\left(A\right),\mathrm{Eigenvalues}\left(J\right)$
 $\left[\begin{array}{r}{2}\\ {2}\\ {0}\\ {0}\end{array}\right]{,}\left[\begin{array}{r}{2}\\ {2}\\ {0}\\ {0}\end{array}\right]$ (2)