The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze
The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze
The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze
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Dual concepts<br />
M = lrm(A,B)<br />
M =<br />
0.32 + 1.3s + 0.95s^2 -0.3 - 1.4s - 0.3s^2 + 0.15s^3<br />
0.63 + 1.3s + 0.63s^2 -0.75 - 1.1s - 0.15s^2 + 0.15s^3<br />
which is verified by<br />
A\M, B\M<br />
ans =<br />
ans =<br />
0.32 + 0.32s -0.3 - 0.15s<br />
0.32 + 0.32s -0.45<br />
0.63 + 0.32s -0.75<br />
0.32 -0.3 + 0.15s-3<br />
<strong>The</strong> dual concepts of right divisors, left multiples, common right divisors, greatest<br />
common right divisors, common left multiples, and least common left multiples are<br />
similarly defined and computed by dual functions grd and llm.<br />
Transposition and conjugation<br />
Transposition<br />
Complex<br />
coefficients<br />
Given<br />
T = [1 0 s^2 s; 0 1 s^3 0]<br />
T =<br />
1 0 s^2 s<br />
0 1 s^3 0<br />
the transposition follows by typing<br />
T.'<br />
ans =<br />
1 0<br />
0 1<br />
s^2 s^3<br />
s 0<br />
<strong>The</strong> command transpose(T)is synonymous with T.'<br />
<strong>The</strong> <strong>Polynomial</strong> <strong>Toolbox</strong> supports polynomial matrices with complex coefficients such<br />
as<br />
C = [1+s 1; 2 s]+i*[s 1; 1 s]<br />
C =<br />
1+0i + (1+1i)s 1+1i<br />
2+1i (1+1i)s<br />
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