Decomposition: Simple and Quadratic Factors

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Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

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

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Covers the integration of rational functions and the decomposition into irreducible factors.

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Covers matrix rank, determinant, and decomposition in linear algebra.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Covers complete and orthonormal families in a Hilbert space, discussing unique projections and vector decomposition.