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Lecture
Gram-Schmidt Process and QR Decomposition
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Orthogonal Bases in Vector Spaces
Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.
Orthogonal Projection: Uniqueness and Properties
Explores the uniqueness and properties of orthogonal projection, including decomposition, associated matrix, linearity, and practical examples.
QR Factorization: Orthogonal Bases and Matrices
Explores QR factorization, orthogonal bases, and matrices for numerical computations and solving systems of equations.
Factorisation QR: Gram-Schmidt Process
Covers the Factorisation QR theorem and the Gram-Schmidt method for orthonormal bases.
Spectral Decomposition
Explores spectral and singular value decompositions of matrices.