Page 10-14
so the main diagonal included only the elements in positions (1,1) and (2,2).
Thus, only the first two elements of the vector were required to form the main
diagonal.
Function VANDERMONDE
Function VANDERMONDE generates the Vandermonde matrix of dimension n
based on a given list of input data. The dimension n is, of course, the length
of the list. If the input list consists of objects {x
1
, x
2
,… x
n
}, then, a
Vandermonde matrix in the calculator is a matrix made of the following
elements:
−
−
−
−
1
2
1
3
2
3
3
1
2
2
2
2
1
1
2
1
1
1
1
1
1
n
n
n
n
n
n
n
x
x
x
x
x
x
x
x
x
x
x
x
L
M
O
M
M
M
L
L
L
For example, the following command in ALG mode for the list {1,2,3,4}:
In RPN mode, enter
{1,2,3,4}
`
VANDERMONDE
.
Function HILBERT
Function HILBERT creates the Hilbert matrix corresponding to a dimension n.
By definition, the n
×
n Hilbert matrix is
H
n
= [h
jk
]
n
×
n
, so that
1
1
−
+
=
k
j
h
jk
