Column End Matrix of a Polynomial Matrix

The column end matrix of an \((m,n)\)-dimensional polynomial matrix \(a(z)=a_0 + a_1 z + \cdots + a_p z^p\) is defined as follows. Suppose that the maximum degree of the elements in the \(i\)-th column is \(p_i\). Then the column end matrix is the \((m,n)\) matrix with \(i\)-th column equal to the \(i\)-th column of the coefficient matrix \(a_{p_i}\). If a column of \(a(z)\) is zero, then the elements of the corresponding column of the column end matrix are set to NA's.

Usage

col_end_matrix(x)

Arguments

x

A polynomial matrix, i.e. an object of class polm.

Value

The column end matrix.

Examples

x = polm(array(c(0,1,1,0,
                 0,0,1,0,
                 0,0,0,1,
                 0,0,0,0), dim = c(2,2,4)))
x
#> ( 2 x 2 ) matrix polynomial with degree <= 3 
#>      z^0 [,1]  [,2] z^1 [,1]  [,2] z^2 [,1]  [,2] z^3 [,1]  [,2]
#> [1,]        0     1        0     1        0     0        0     0
#> [2,]        1     0        0     0        0     1        0     0
degree(x)
#>      [,1] [,2]
#> [1,]   -1    1
#> [2,]    0    2
degree(x, 'columns')
#> [1] 0 2
col_end_matrix(x)
#>      [,1] [,2]
#> [1,]    0    0
#> [2,]    1    1