Matvec Users’ Guide

56 CHAPTER 9. MACRO PACKAGES
Row 1 1 2 3
Row 2 2 3 0
Row 3 3 0 0
> hankel([1,2,3],[3,4,5])
Col 1 Col 2 Col 3
Row 1 1 2 3
Row 2 2 3 4
Row 3 3 4 5
9.3.4 vander
vander(C) returns the Vandermonde matrix whose second to last column is C. The j-th column of a Vandermonde
matrix is given by A(∗, j) = C ( n − j). For example,
> package("special_matrix");
> vander([1,2,3])
Col 1 Col 2 Col 3
Row 1 1 1 1
Row 2 4 2 1
Row 3 9 3 1
9.3.5 hadamard
hadamard(k) return the Hadamard matrix of order n = 2 k .
not available
9.3.6 pascal
pascal(n) returns the Pascal matrix of order n: a symmetric positive definite matrix with integer entries,
made up from Pascal’s triangle. For example,
> package("special_matrix");
> pascal(3)
Col 1 Col 2 Col 3
Row 1 1 1 1
Row 2 1 2 3
Row 3 1 3 6
9.3.7 toeplitz
toeplitz(C) returns a symmetric (or Hermitian) Toeplitz matrix; whereas toeplitz(C,R) returns a nonsymmetric
Toeplitz matrix having C as its first column and R as its first row. For example,
> package("special_matrix");
> toeplitz([1,2,3])
Col 1 Col 2 Col 3
Row 1 1 2 3
Row 2 2 1 2
Row 3 3 2 1