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Related lectures (32)

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Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Signal Representations

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Hermitian Operators and Spectral Theorem

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.