The Resultant, Episode 3

Last time the linear operator

Φ: *K _{n}*[

*x*]⊕

*K*[

_{m}*x*] →

*K*[

_{m+n}*x*]

Φ(

*p*,

*q*)=

*pE+qF*

made its grand entrance, clothed in the *Sylvester matrix*. (Recall that *K _{n}*[

*x*] is the vector space of all polynomials of degree <

*n*with coefficients in

*K*, likewise for

*K*[

_{m}*x*] and

*K*[

_{m+n}*x*].)