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Sylvester Matrix

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Sylvester Matrix

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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
 
For more information, see http://en.wikipedia.org/wiki/Sylvester_matrix
 
See also gallery, toeplitz
             circulant (File Exchange)
 

MATLAB release MATLAB 7.6 (R2008a)
Other requirements should work on most ML releases
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Comments and Ratings (2)
07 Jun 2013 Jos (10584)

The error mentioned by Paul has been fixed in version 3.0

03 Jun 2013 Paul

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

Updates
06 Jun 2013

fixed serious error resulting in non-square outcomes in some situations

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