Lectures related to Polynomial Division Approach & Observer Control

Minimal Polynomials: Uniqueness and Division

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

Polynomial Division & Observer/Controller Approach

Covers polynomial division and observer/controller approach with step-by-step examples.

Division Polynomials: Theorems and Applications

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

Polynomial Methods: GCD Calculation Summary

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

Decomposition of Linear Operators

Covers the decomposition of linear operators and properties of eigenspaces.

Eigenvalues and Eigenvectors

Covers eigenvalues, eigenvectors, and their applications in linear algebra.

Polynomials and Endomorphisms

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

State Observers Intro

Introduces state observers for estimating the state from input and output measurements.

Stability: Poles, Zeros, and Control

Covers stability, poles, zeros, and control in dynamic systems, emphasizing the importance of observability.

Polynomials: Roots and Factorization

Covers polynomial roots, factorization, and unique representation through examples of polynomial division with remainders.

State-Space Representation: Controllability and Observability

Explores state-space representation, controllability, observability, and regulator calculation using the Ackermann method.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Polynomial Division: Terms and Factors

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Examples: Polynomial Factorization

Covers polynomial factorization examples and polynomial division in complex numbers.

State-Space Representation: Structure Theorem

Covers the structure theorem for state-space representations and companion forms.

Algebraic Geometry: Rings and Bodies

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Polynomial Roots: Finding Solutions and Division

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

Factorisation: The Fundamental Theorem of Algebra

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

Euclidean Division: Uniqueness and Remainder

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