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Lecture
Spectral Theorem: Second
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Orthonormal Bases in Hilbert Spaces
Explores orthonormal bases in Hilbert spaces, discussing their properties and generation using the Gram-Schmidt method.
Spectral Decomposition
Explores spectral and singular value decompositions of matrices.
Diagonalization of Symmetric Matrices
Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.
Spectral Theorem Recap
Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.
Diagonalization of Symmetric Matrices
Explores the diagonalization of symmetric matrices and the orthogonality of eigenvectors.
Spectral Theorem: Eigenvalues and Eigenvectors
Covers the spectral theorem, eigenvalues, eigenvectors, and their importance in linear algebra.
Quantum Mechanics: Postulates and Observables
Explains the postulates of quantum mechanics and the representation of observables by operators.
Hilbert Space: Geometry, Bases
Explores Hilbert space, scalar product, geometry, bases, complex functions, and quantum mechanics applications.
Decomposition Spectral: Symmetric Matrices
Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.
Subspaces, Spectra, and Projections
Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.
