jordan - Maple Help

MTM

 jordan
 compute the Jordan form of a matrix

 Calling Sequence J = jordan(A) [V,J] = jordan(A)

Parameters

 A - square matrix

Description

 • The function jordan(A) computes the Jordan form of a matrix A.
 • When the function is called using the form J = jordan(A), the returned value of J is the Jordan form of the matrix A.
 • When the function is called using the form [V,J] = jordan(A), the returned value of J is the Jordan form of the matrix A, and the returned value of V is the transformation matrix corresponding to this Jordan form.

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $A≔\mathrm{Matrix}\left(\left[\left[1,2,1\right],\left[2,4,2\right],\left[2,8,1\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{ccc}{1}& {2}& {1}\\ {2}& {4}& {2}\\ {2}& {8}& {1}\end{array}\right]$ (1)
 > $J≔\mathrm{jordan}\left(A\right)$
 ${J}{≔}\left[\begin{array}{ccc}{0}& {0}& {0}\\ {0}& {3}{-}\sqrt{{22}}& {0}\\ {0}& {0}& {3}{+}\sqrt{{22}}\end{array}\right]$ (2)
 > $V,J≔\mathrm{jordan}\left(A\right)$
 ${V}{,}{J}{≔}\left[\begin{array}{ccc}\frac{{12}{}\sqrt{{22}}}{\left({22}{+}{3}{}\sqrt{{22}}\right){}\left({-}{3}{+}\sqrt{{22}}\right)}& \frac{{-}{10}{+}\sqrt{{22}}}{{2}{}\left({22}{+}{3}{}\sqrt{{22}}\right){}\left({-}{3}{+}\sqrt{{22}}\right)}& \frac{{4}{+}\sqrt{{22}}}{{2}{}\left({22}{+}{3}{}\sqrt{{22}}\right)}\\ {-}\frac{{2}{}\sqrt{{22}}}{\left({22}{+}{3}{}\sqrt{{22}}\right){}\left({-}{3}{+}\sqrt{{22}}\right)}& \frac{{-}{10}{+}\sqrt{{22}}}{\left({22}{+}{3}{}\sqrt{{22}}\right){}\left({-}{3}{+}\sqrt{{22}}\right)}& \frac{{4}{+}\sqrt{{22}}}{{22}{+}{3}{}\sqrt{{22}}}\\ {-}\frac{{8}{}\sqrt{{22}}}{\left({22}{+}{3}{}\sqrt{{22}}\right){}\left({-}{3}{+}\sqrt{{22}}\right)}& \frac{{-}{1}{+}{4}{}\sqrt{{22}}}{\left({22}{+}{3}{}\sqrt{{22}}\right){}\left({-}{3}{+}\sqrt{{22}}\right)}& \frac{{7}{+}\sqrt{{22}}}{{22}{+}{3}{}\sqrt{{22}}}\end{array}\right]{,}\left[\begin{array}{ccc}{0}& {0}& {0}\\ {0}& {3}{-}\sqrt{{22}}& {0}\\ {0}& {0}& {3}{+}\sqrt{{22}}\end{array}\right]$ (3)