Matricizations and Alternating Least Squares

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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.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Rings and Modules

Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.

Matrix Multiplication: Basics and Properties

Covers the basics of matrix multiplication, including properties and examples.

Linear Algebra: Matrix Operations

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Matrix Operations: Product and Inverse

Covers matrix operations, focusing on the product and inverse of matrices.

Continuum Mechanics: Tensor Analysis and Kinematics

Covers tensor analysis, kinematics, and fluid mechanics in continuum mechanics.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.