Extension of Linear Transformations

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Adjoint of Linear Operators on Inner Product Spaces

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Essential Operators: Spectrum and Resolvent Set

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

Linear Maps and the Duality Principle in Mathematics

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

Linear Operators: Boundedness and Convergence

Explores linear operators, boundedness, and convergence in Banach spaces, focusing on Cauchy sequences and operator identification.

Functional Calculus: Operator Definition and Properties

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Fourier Transform: Schwartz Space

Covers the Fourier transform on Schwartz space and its properties, including continuity and linearity, as well as the density of smooth compactly supported functions.

The Closed Graph Theorem

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.

Harmonic Forms: Main Theorem

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