Sylvester Matrix

This Demonstration shows the Sylvester matrix of two polynomials and of positive degrees and .
The entries of the first row are the coefficients of from highest to lowest power filled out by zeros on the right. The next rows rotate each preceding row to the right, so that the last row ends with the constant term . The last rows are similar, using the coefficients of . See Related Links, "Sylvester Matrix" for a symbolic example.
The determinant of the Sylvester matrix of two polynomials is the resultant of the polynomials (see Related Links).
The polynomials and have a common root if and only if their resultant is zero (see Related Links).
If , the resultant of and equals [1, pp. 704–707].



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


[1] D. Kurepa, High Algebra, Book 1 (in Croatian), Zagreb: Skolska knjiga, 1965.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+