Bases: Linear Combinations and Function Spaces

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Related lectures (26)

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Orthogonal/Orthonormal Bases and Polynomials

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

Projection in Vector Spaces

Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.

Finding Orthogonal/Orthonormal Base: First Step

Introduces the first step in finding an orthogonal/orthonormal base in a vector space.

Linear Algebra: Lecture Notes

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Orthogonal Sets and Bases

Introduces orthogonal sets and bases, discussing their properties and linear independence.

Orthogonal Bases in Vector Spaces

Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.

Vector Spaces Equivalence

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Matrix Operations and Orthogonality

Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.

Orthogonal Bases in Vector Spaces

Covers the concept of orthogonal bases in vector spaces and Pythagorean theorem applications.