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Matrices 479
Hilbert Given a positive integer, n, returns the n
th
order Hilbert
matrix. Each element of the matrix is given by the formula
1/(j+k-1) where j is the row number and k is the column
number.
hilbert(n)
Example:
In CAS view, hilbert(4) returns
Isometric Matrix of an isometry given by its proper elements.
mkisom(vector,sign(1 or -1))
Example:
In CAS view, mkisom([1,2],1) returns
Vandermonde Returns the Vandermonde matrix. Given a vector [n1, n2
… nj], returns a matrix whose first row is [(n1)
0
, (n1)
1
,
(n1)
2
, …,(n1)
j-1
]. The second row is [(n2)
0
, (n2)
1
, (n2)
2
,
…,(n2)
j-1
], etc.
vandermonde(vector)
Example:
vandermonde([1 3 5]) returns
Basic
Norm Returns the Frobenius norm of a matrix.
|matrix|
Example:
returns 5.47722557505
1
1
2
-
1
3
-
1
4
-
1
2
-
1
3
-
1
4
-
1
5
-
1
3
-
1
4
-
1
5
-
1
6
-
1
4
-
1
5
-
1
6
-
1
7
-
1cos 1sin–
1sin 1cos
11 1
13 9
1525
12
34