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LinearAlgebra

 JordanBlockMatrix
 construct a Matrix of Jordan blocks

 Calling Sequence JordanBlockMatrix(K, d, options)

Parameters

 K - list of ordered pairs of the form [eigenvalue, dimension] d - (optional) non-negative integer; dimension of the resulting Matrix options - (optional); constructor options for the result object

Description

 • The JordanBlockMatrix(K) function, where K is a list of ordered pairs [a, b], constructs a Matrix in which each diagonal block is a b-dimensional Jordan block defined by a.
 • The JordanBlockMatrix(K, d) function acts like JordanBlockMatrix(K) except that a d x d Matrix is returned.
 • The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).
 By default, the JordanBlockMatrix function constructs a Matrix by using the band[0, 1] shape and storage.
 • This function is part of the LinearAlgebra package, and so it can be used in the form JordanBlockMatrix(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[JordanBlockMatrix](..).

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\right):$
 > $\mathrm{JordanBlockMatrix}\left(\left[\left[x,3\right],\left[5,1\right],\left[y,2\right]\right]\right)$
 $\left[\begin{array}{cccccc}{x}& {1}& {0}& {0}& {0}& {0}\\ {0}& {x}& {1}& {0}& {0}& {0}\\ {0}& {0}& {x}& {0}& {0}& {0}\\ {0}& {0}& {0}& {5}& {0}& {0}\\ {0}& {0}& {0}& {0}& {y}& {1}\\ {0}& {0}& {0}& {0}& {0}& {y}\end{array}\right]$ (1)
 > $\mathrm{JordanBlockMatrix}\left(\left[\left[2,2\right],\left[3,2\right]\right],5\right)$
 $\left[\begin{array}{ccccc}{2}& {1}& {0}& {0}& {0}\\ {0}& {2}& {0}& {0}& {0}\\ {0}& {0}& {3}& {1}& {0}\\ {0}& {0}& {0}& {3}& {0}\\ {0}& {0}& {0}& {0}& {0}\end{array}\right]$ (2)