Minimal Polynomials: Uniqueness and Division

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Examples: Polynomial Factorization

Covers polynomial factorization examples and polynomial division in complex numbers.

Factorisation: The Fundamental Theorem of Algebra

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

System Equivalence

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Polynomial Factorization: Field Approach

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

Polynomial Division & Observer/Controller Approach

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

Euclidean Division and Simple Elements

Explains polynomial division, factor decomposition, and rational function simplification.

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.