Polynomial Approximation: Orthonormal Basis and Projection

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

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Covers the theorems related to orthogonal projection and orthonormal bases.

Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Explains orthogonal families, bases, and projections in vector spaces.

Series covers spherical coordinates, harmonics, Legendre polynomials, and angular momentum.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Explores orthogonal projection in Euclidean space, emphasizing uniqueness and calculation methods.