Quadratic Approximation: Example

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Orthogonal Bases and Projection

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

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.

Gram-Schmidt Process

Introduces the Gram-Schmidt orthogonalization process to find orthogonal bases for vector subspaces.

Orthogonal/Orthonormal Bases and Polynomials

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

Orthogonal Bases in Vector Spaces

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

Orthogonalization of Vectors

Covers the Gram-Schmidt orthogonalization process and vector projections in a vector space.

Orthogonal Vectors and Projections

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

Orthogonal Complement and Projection

Covers the concept of orthogonal complement and projection in vector spaces.

Development Limit: Order 1 and 2

Covers limited order 1 and 2 development, focusing on linearity and polynomial approximation.

Orthogonal Projection: Example and Additional Remarks

Explains orthogonal projection onto a subspace and finding orthogonal bases using Gram-Schmidt procedure.