Advanced Analysis II: Eigenvalues and Compact Sets

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Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Explores the diagonalization of matrices through eigenvectors and eigenvalues.

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Covers distribution interpolation spaces, including the regularized flux and extension operators.

Explores the demonstration of a theorem on compact functions and non-regular boundaries.

Explores matrices, eigenvalues, and diagonalizability, including invertibility and vector spaces.

Covers normed vector spaces, including definitions, properties, examples, and sets in normed spaces.

Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.

Explores real functions, covering continuity, supremum, infimum, maximum, minimum, compact and connected sets, and the intermediate value theorem.

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.