Proof of Schmidt Theorem and Entropy Properties

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Introduces Banach spaces for geometric potentials and pressure analysis, emphasizing equilibrium states and pressure function analyticity.

Information Measures: Entropy and Information Theory

Explains how entropy measures uncertainty in a system based on possible outcomes.

Variational Formulation: Information Measures

Explores variational formulation for measuring information content and divergence between probability distributions.

Von Neumann Entropy: Mixed State and Density Matrix

Explores Von Neumann Entropy in mixed states and density matrices, including quantum bits and entangled systems.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Bipartite systems - Entanglement

Covers the concept of entanglement in bipartite systems, focusing on entropy and Schmidt decomposition.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Information Measures

Covers information measures like entropy and Kullback-Leibler divergence.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Density Matrix: Statistical Mixtures

Covers density matrix and statistical mixtures in quantum systems, emphasizing the importance of understanding the statistical mixture of states.