ConstantMatrix - Maple Help

LinearAlgebra

 ConstantMatrix
 construct a constant Matrix
 ConstantVector
 construct a constant Vector

 Calling Sequence ConstantMatrix(s, r, c, cpt, options) ConstantVector[o](s, d, cpt, options)

Parameters

 s - algebraic expression; constant value in the Matrix or Vector r - (optional) non-negative integer; row dimension of the resulting Matrix c - (optional) non-negative integer; column dimension of the resulting Matrix d - (optional) non-negative integer; dimension of the resulting Vector cpt - (optional) equation of the form compact=true or false; selects the compact form of the output options - (optional); constructor options for the result object [o] - (optional) use either [row] or [column]; specifies the orientation of the resulting Vector

Description

 • The ConstantMatrix(s, r, c) function returns an r x c Matrix in which all of the entries have the value s.
 If the row dimension is not provided, it defaults to zero. If the column dimension is not provided, it defaults to the row dimension.
 • The ConstantVector(s, d) function returns a d-dimensional column Vector in which all of the entries have the value s.
 The ConstantVector[row](s, d) function acts like ConstantVector(s, d) except that a row Vector is returned.  If the orientation option is omitted or if ConstantVector[column](s, d) is used, a column Vector is returned.
 If the dimension is not provided, it defaults to zero.
 • If the compact option (cpt) is omitted, or, if it is included in the calling sequence as just the symbol compact or in the form compact=true, then the result is built by using a shape function designed to minimize storage. If the option is entered as compact=false, a full rectangular object is constructed.
 • The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix or Vector 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).
 If a shape value is not provided, then the shape of the resulting object is determined by the compact option. Otherwise, a result with the specified shape is constructed with all values set to const via the fill parameter to the Matrix (or Vector) constructor.
 If readonly=false is included, it is ignored unless the default shape (constant[const]) is overridden by also including a mutable shape in options.
 • This function is part of the LinearAlgebra package, and so it can be used in the form ConstantMatrix(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[ConstantMatrix](..).

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\right):$
 > $\mathrm{ConstantMatrix}\left(4,5,2\right)$
 $\left[\begin{array}{cc}{4}& {4}\\ {4}& {4}\\ {4}& {4}\\ {4}& {4}\\ {4}& {4}\end{array}\right]$ (1)
 > $\mathrm{ConstantMatrix}\left(n,4,\mathrm{shape}=\mathrm{triangular}\left[\mathrm{upper}\right]\right)$
 $\left[\begin{array}{cccc}{n}& {n}& {n}& {n}\\ {0}& {n}& {n}& {n}\\ {0}& {0}& {n}& {n}\\ {0}& {0}& {0}& {n}\end{array}\right]$ (2)
 > $v≔\mathrm{ConstantVector}\left[\mathrm{row}\right]\left(x,4\right)$
 ${v}{≔}\left[\begin{array}{cccc}{x}& {x}& {x}& {x}\end{array}\right]$ (3)
 > $\mathrm{VectorOptions}\left(v,\mathrm{shape}\right)$
 $\left[{{\mathrm{constant}}}_{{x}}\right]$ (4)
 > $\mathrm{v2}≔\mathrm{ConstantVector}\left(3,2,\mathrm{compact}=\mathrm{false}\right)$
 ${\mathrm{v2}}{≔}\left[\begin{array}{c}{3}\\ {3}\end{array}\right]$ (5)
 > $\mathrm{VectorOptions}\left(\mathrm{v2},\mathrm{shape}\right)$
 $\left[\right]$ (6)