Polynomial Division & Observer/Controller Approach

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Related lectures (46)

Polynomial Methods: GCD Calculation Summary

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

Euclidean Algorithm

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

Ideals: Polynomials and Definitions

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

Polynomials: Roots and Factorization

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

Polynomial Factorization over Finite Fields

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

Minimal Polynomials: Uniqueness and Division

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

Euclid and Bézout: Algorithms and Theorems

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

Polynomials and Endomorphisms

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

Polynomial Roots: Finding Solutions and Division

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

Polynomial Division Approach & Observer Control

Covers the RST approach using polynomial division for system adjustment.

Euclidean Division: Uniqueness and Remainder

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

Factorisation: The Fundamental Theorem of Algebra

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

Polynomials: Definition and Operations

Covers polynomials, their operations, division theorem, and provides illustrative examples.

System Equivalence

Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Decomposition of Linear Operators

Covers the decomposition of linear operators and properties of eigenspaces.

Number Theory: Quiz

Covers fundamental concepts in number theory with examples and quizzes.

Number Theory: GCD and LCM

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

Polynomial Division: Terms and Factors

Covers polynomial division, terms, factors, and integration methods.

Polynomial Factorization: Field Approach Log in to Mediaspace to watch this video

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

Polynomial Rings and Irreducibility Criteria Log in to Mediaspace to watch this video

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

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