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Lecture
Gram-Schmidt Process
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Orthogonal Families and Projections
Introduces orthogonal families, orthonormal bases, and projections in linear algebra.
Orthogonal Projection: Example and Additional Remarks
Explains orthogonal projection onto a subspace and finding orthogonal bases using Gram-Schmidt procedure.
Orthogonal Bases in Vector Spaces
Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.
Orthogonal Projection Theorem
Explores orthogonal projection calculation and orthonormal bases uniqueness through matrix operations.
Orthogonal Projection: Spectral Decomposition
Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.
Orthogonal Bases in Vector Spaces
Covers orthogonal bases, Gram-Schmidt method, linear independence, and orthonormal matrices in vector spaces.
Orthogonal Projection on Vector Subspace
Explains orthogonal projection on a vector subspace in Euclidean space.
Finding Orthogonal/Orthonormal Base: First Step
Introduces the first step in finding an orthogonal/orthonormal base in a vector space.
Matrix Operations and Orthogonality
Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.
Vector Calculus in 3D
Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.