Advanced Analysis II: Matrix Diagonalization

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Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Explores compact sets, extreme values, and function theorems on bounded sets.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Covers Jordan-measurable sets, Riemann-integrability, and function continuity on compact sets.

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

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

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 the description of problem solutions and the concept of compactness and uniform continuity.