Identity - Maple Help

LinearAlgebra[Modular]

 Identity
 create mod m identity Matrix

 Calling Sequence Identity(m, n, dtype, order)

Parameters

 m - modulus n - number of rows and columns in output identity Matrix dtype - datatype of output object order - (optional) ordering of output object

Description

 • The Identity function creates a mod m identity Matrix of the specified type and dimensions.
 • The allowable datatypes are hardware integer (dtype=integer[4]/integer[8] or integer[]), hardware float (dtype=float[8]), or Maple integer (dtype=integer). If specified, order can be C_order or Fortran_order. If not specified, C_order is used.
 • This command is part of the LinearAlgebra[Modular] package, so it can be used in the form Identity(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][Identity](..).

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Modular}\right]\right):$
 > $\mathrm{A1}≔\mathrm{Identity}\left(31,20,\mathrm{integer}\left[\right]\right)$
 ${\mathrm{A1}}{≔}\begin{array}{c}\left[\begin{array}{ccccccccccc}{1}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {\dots }\\ {0}& {1}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {\dots }\\ {0}& {0}& {1}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {\dots }\\ {0}& {0}& {0}& {1}& {0}& {0}& {0}& {0}& {0}& {0}& {\dots }\\ {0}& {0}& {0}& {0}& {1}& {0}& {0}& {0}& {0}& {0}& {\dots }\\ {0}& {0}& {0}& {0}& {0}& {1}& {0}& {0}& {0}& {0}& {\dots }\\ {0}& {0}& {0}& {0}& {0}& {0}& {1}& {0}& {0}& {0}& {\dots }\\ {0}& {0}& {0}& {0}& {0}& {0}& {0}& {1}& {0}& {0}& {\dots }\\ {0}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {1}& {0}& {\dots }\\ {0}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {0}& {1}& {\dots }\\ {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {}\end{array}\right]\\ \hfill {\text{20 × 20 Matrix}}\end{array}$ (1)
 > $\mathrm{A2}≔\mathrm{Identity}\left(31,20,\mathrm{float}\left[8\right],\mathrm{Fortran_order}\right)$
 ${\mathrm{A2}}{≔}\begin{array}{c}\left[\begin{array}{ccccccccccc}{1.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {\dots }\\ {0.}& {1.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {\dots }\\ {0.}& {0.}& {1.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {\dots }\\ {0.}& {0.}& {0.}& {1.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {\dots }\\ {0.}& {0.}& {0.}& {0.}& {1.}& {0.}& {0.}& {0.}& {0.}& {0.}& {\dots }\\ {0.}& {0.}& {0.}& {0.}& {0.}& {1.}& {0.}& {0.}& {0.}& {0.}& {\dots }\\ {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {1.}& {0.}& {0.}& {0.}& {\dots }\\ {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {1.}& {0.}& {0.}& {\dots }\\ {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {1.}& {0.}& {\dots }\\ {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {0.}& {1.}& {\dots }\\ {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {}\end{array}\right]\\ \hfill {\text{20 × 20 Matrix}}\end{array}$ (2)
 > $\mathrm{A3}≔\mathrm{Identity}\left(31,3,\mathrm{integer}\right)$
 ${\mathrm{A3}}{≔}\left[\begin{array}{ccc}{1}& {0}& {0}\\ {0}& {1}& {0}\\ {0}& {0}& {1}\end{array}\right]$ (3)
 > $\mathrm{A4}≔\mathrm{Identity}\left(31,5,\mathrm{float}\left[8\right]\right)$
 ${\mathrm{A4}}{≔}\left[\begin{array}{ccccc}{1.}& {0.}& {0.}& {0.}& {0.}\\ {0.}& {1.}& {0.}& {0.}& {0.}\\ {0.}& {0.}& {1.}& {0.}& {0.}\\ {0.}& {0.}& {0.}& {1.}& {0.}\\ {0.}& {0.}& {0.}& {0.}& {1.}\end{array}\right]$ (4)