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[project @ 2004-09-22 02:50:35 by jwe]
author jwe
date Wed, 22 Sep 2004 02:50:36 +0000
parents 22bd65326ec1
children c08cb1098afc
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5015:6d481b6e349e 5016:bdbee5282954
19 19
20 ## -*- texinfo -*- 20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {} vander (@var{c}) 21 ## @deftypefn {Function File} {} vander (@var{c})
22 ## Return the Vandermonde matrix whose next to last column is @var{c}. 22 ## Return the Vandermonde matrix whose next to last column is @var{c}.
23 ## 23 ##
24 ## A Vandermonde matrix has the form 24 ## A Vandermonde matrix has the form:
25 ## @iftex 25 ## @iftex
26 ## @tex 26 ## @tex
27 ## $$ 27 ## $$
28 ## \left[\matrix{c_0^n & \ldots & c_0^2 & c_0 & 1\cr 28 ## \left[\matrix{c_1^{n-1} & \cdots & c_1^2 & c_1 & 1 \cr
29 ## c_1^n & \ldots & c_1^2 & c_1 & 1\cr 29 ## c_2^{n-1} & \cdots & c_2^2 & c_2 & 1 \cr
30 ## \vdots & & \vdots & \vdots & \vdots\cr 30 ## \vdots & \ddots & \vdots & \vdots & \vdots \cr
31 ## c_n^n & \ldots & c_n^2 & c_n & 1}\right]. 31 ## c_n^{n-1} & \cdots & c_n^2 & c_n & 1 }\right]
32 ## $$ 32 ## $$
33 ## @end tex 33 ## @end tex
34 ## @end iftex 34 ## @end iftex
35 ## @ifinfo 35 ## @ifinfo
36 ## 36 ##
37 ## @example 37 ## @example
38 ## @group 38 ## @group
39 ## c(0)^n ... c(0)^2 c(0) 1 39 ## c(1)^(n-1) ... c(1)^2 c(1) 1
40 ## c(1)^n ... c(1)^2 c(1) 1 40 ## c(2)^(n-1) ... c(2)^2 c(2) 1
41 ## . . . . 41 ## . . . . .
42 ## . . . . 42 ## . . . . .
43 ## . . . . 43 ## . . . . .
44 ## 44 ## c(n)^(n-1) ... c(n)^2 c(n) 1
45 ## c(n)^n ... c(n)^2 c(n) 1
46 ## @end group 45 ## @end group
47 ## @end example 46 ## @end example
48 ## @end ifinfo 47 ## @end ifinfo
49 ## @end deftypefn 48 ## @end deftypefn
50 ## @seealso{hankel, sylvester_matrix, hilb, invhilb, and toeplitz} 49 ## @seealso{hankel, sylvester_matrix, hilb, invhilb, and toeplitz}