Create a companion matrix from a vector

Create a companion matrix from a vector.

Usage

companion_matrix(v, ncol = length(v), nrow = ncol)

Arguments

v

the first row of the matrix, a numeric vector or a matrix with one row.

ncol

number of columns, a number.

nrow

number of rows, a number.

Details

With the default settings, a square \(m\times m\) matrix is returned, where \(m\) is the length of v. If ncol>\(m\), the vector is amended with 0's. It is an error for ncol to be smaller than \(m\).

Argument nrow may be used to get a rectangular matrix, although the term "companion" is normally used only for square matrices.

Value

a matrix

Examples

companion_matrix(4:1)
#>      [,1] [,2] [,3] [,4]
#> [1,]    4    3    2    1
#> [2,]    1    0    0    0
#> [3,]    0    1    0    0
#> [4,]    0    0    1    0
companion_matrix(4:1, ncol=6)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    4    3    2    1    0    0
#> [2,]    1    0    0    0    0    0
#> [3,]    0    1    0    0    0    0
#> [4,]    0    0    1    0    0    0
#> [5,]    0    0    0    1    0    0
#> [6,]    0    0    0    0    1    0
companion_matrix(4:1, ncol=6, nrow=3)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    4    3    2    1    0    0
#> [2,]    1    0    0    0    0    0
#> [3,]    0    1    0    0    0    0