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Lecture
Orthogonal Basis in W
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Curves in the Oriented Plane
Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
Sylvester's Theorem: Orthogonal Bases
Explores Sylvester's Theorem and the importance of orthogonal bases in linear algebra.
Hilbert Spaces: Orthonormal Systems
Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.
Orthogonal Projection: Example and Additional Remarks
Explains orthogonal projection onto a subspace and finding orthogonal bases using Gram-Schmidt procedure.
Linear Independence and Bases in Vector Spaces
Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.
Orthogonality and Scalar Product
Explores orthogonality, scalar product, and orthonormal bases in vector spaces.