Linear Maps and the Duality Principle in Mathematics

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

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

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

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

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

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

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.