POLYNOMIALS Archives

Solving Polynomial Equations: Finding q(uv) = 0

Discover how to solve polynomial equations and find q(uv) = 0. Learn techniques for determining polynomial relationships between variables. Polynomial Equation Solver.

Polynomial Matrix Decomposition: A Step-by-Step Guide

Learn how to decompose polynomial matrices using elementary row operations. This guide provides a step-by-step approach to polynomial matrix decomposition.

Understanding Inequalities in Harmonic Homogeneous Polynomials

Explore the inequality concerning the dimension of harmonic homogeneous polynomials. Learn about the relationship between homogeneous polynomials and their Laplacian. Harmonic Homogeneous Polynomials explained.

Polynomial Ratio Image: Exploring the Image of a Ratio of Polynomials in ℂ

Investigating the image of a ratio of polynomials with affine coefficients. Does the image lie within a complex polytope defined by vertices? Polynomial Ratio Image.

Chebyshev Polynomials Series: Exploring Patterns in Polynomial Coefficients

Discover the fascinating relationship between Chebyshev polynomials of the second kind and binomial coefficients in this exploration of series. Chebyshev Polynomials Series.

Non-commutative Product Expansion: Rewriting Products as Sums

Learn how to rewrite a non-commutative product as a sum. This guide explores methods for expanding products of non-commuting elements offering both general formulas and recursive approaches. Non-commutative Product Expansion explained.

Computing the Ideal of a Projective Algebraic Set in P^2(C)

Learn how to compute the ideal of a projective algebraic set in P^2(C). This post explores methods for determining the ideal including geometric approaches and Gröbner bases. Projective Algebraic Set Ideal.

Calculating the Change of Basis Matrix for Linear Maps on Polynomials

Learn how to calculate the change of basis matrix for linear maps on polynomials. This guide clarifies common discrepancies and misunderstandings. Change of Basis Matrix explained.