Linear Operators: Quantum Mechanics and Linear Algebra

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Related lectures (32)

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Quantum Mechanics: Mathematical Framework

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Quantum Mechanics: Self-adjoint Operators and Quantum Information

Offers a crash course on quantum mechanics, emphasizing self-adjoint operators and quantum information.

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

The Hessian and Newton's method

Covers the Hessian and Newton's method for optimization using iterative processes.

Eigenvalues and Eigenvectors in 3D

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Eigenvalues and Eigenvectors: Understanding Matrix Properties

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Linear Algebra: Unitary Operators

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

Common Orthonormal Eigenbasis to Normal Commuting Operators

Discusses the existence of a common orthonormal eigenbasis to normal operators.

Linear Operators: Boundedness and Spaces

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

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