Polynomial Factorization over a Field: Eigenvalues

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Page 3 of 4

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

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

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

Explores complex number properties, roots, and polynomial equations in the complex plane.

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

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

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

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

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