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Lecture
The Fundamental Theorem of Algebra
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Related lectures (28)
Complex Roots: Conjugate Pairs and Quadratic Equations
Explores complex roots, conjugate pairs, and quadratic equations solving strategies.
Complex Roots and Polynomials
Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.
Complex Numbers: Roots and Polynomials
Covers the properties of complex numbers, including finding roots and factorizing polynomials.
Polynomials with Real Coefficients
Explores polynomials with real coefficients, complex roots, and sequences' properties.
Complex Polynomials and Factorization
Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.
Factorisation: Real Coefficients Examples
Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.
Polynomials: Definitions and Operations
Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.
Integration on H_pxH and Arithmetic
Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.
Complex Factorization Examples
Explores complex polynomial factorization examples, demonstrating the process and implications of complex roots in real polynomials.
Factorisation: Polynomials and Theorem
Covers irreducible polynomials, fundamental theorem of algebra, and factorization in complex and real polynomials.
Complex Eigenvalues Appendix
Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.
Complex Numbers: Operations and Applications
Explores complex number properties, roots, and polynomial equations in the complex plane.
Polynomials and Endomorphisms
Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.
Linear Combinations and Vector Spaces
Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.
Linear Algebra: Abstract Concepts
Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.
Complex Plane and Polynomials
Covers the complex plane, operations, transformations, and complex polynomials.
Integration: Simple Elements
Covers the integration of simple elements using various techniques to solve integration problems.
Fundamental Theorem of Algebra
Covers the Fundamental Theorem of Algebra, complex sequences, convergence, and continuity of functions.
Differentiable Functions and Lagrange Multipliers
Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.
Irreducibility Criteria in Rings
Explores irreducibility criteria in rings, emphasizing linear and reducible polynomials.
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