Lectures related to Functional Analysis I

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

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

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Explores matrices, change of bases, eigenvectors, eigenvalues, and vector spaces.

Covers the reduction of matrices, eigenvalues, eigenvectors, and geometric interpretations in vector spaces.

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Explores symmetric linear operators, eigenvalues, and eigenvectors in functional analysis.

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