Lectures related to Polynomial Division & Observer/Controller Approach

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Covers polynomial rings, irreducibility criteria, and algebraic structures in fields.

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Explains how to find solutions for polynomial equations and perform polynomial division.

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Covers the RST approach using polynomial division for system adjustment.

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores well ordering, induction, Euclidean division, and prime factorization in integers.