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Sylvester Matrix

Jos (10584) (view profile)

15 May 2009 (Updated )

SYLVESTER - Sylvester matrix of two polynomials (v3.0, june 2013)

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Description

S = SYLVESTER(P,Q) returns the Sylvester matrix S that is associated with the two polynomial representations P and Q, of degree Dp and Dq, respectively. S is a (Dp+Dq)-by-(Dp+Dq) square matrix. Note that the degree of the polynomial is one less the the number of elements of its representation: degree(P) = numel(P)-1.

SYLVESTER(P,Q, [Mp Mq]) returns a generalization by specifiying the size. The Sylvester matrix S will be a, in general non-square, (Mp+Mq)-by-K matrix, with K being the maximum of (Mp+Dp) and (Mq+Dq).

Examples:
P = [1 2 3 4] ; Q = [6 7] ; % Dp = 3, Dq = 1 ;
M = sylvester(P,Q)
% 1 2 3 4
% 6 7 0 0
% 0 6 7 0
% 0 0 6 7

M = sylvester([1 0 3],[2 4],[3 1])
% -> a non-square sylvester matrix
% 1 0 3 0 0
% 0 1 0 3 0
% 0 0 1 0 3
% 2 4 0 0 0

circulant (File Exchange)

MATLAB release MATLAB 7.6 (R2008a)
Other requirements should work on most ML releases
07 Jun 2013 Jos (10584)

Jos (10584) (view profile)

The error mentioned by Paul has been fixed in version 3.0

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03 Jun 2013 Paul

Paul (view profile)

Does not work but is easily corrected.
Change to : zeros(NQ-2,1)],zeros(NQ-1,1)); etc

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