Kernel Methods: Representer Theorem & ERM

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Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

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.

Robust Optimization: Polynomial Optimization

Explores polynomial optimization, including writing polynomials as matrix products and solving linear equations for nonnegativity.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Quadratic Forms in IR³

Explores quadratic forms in IR³, matrix properties, diagonalization, and positive definite matrices.

Dynamic Programming: Rod Cutting and Matrix Chain Multiplication

Introduces dynamic programming with a focus on rod cutting and matrix chain multiplication.

Orthogonal Linear Maps

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Matrix Operations: Composition and Product

Covers the composition and product of matrices, including matrix multiplication.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Density Operator: Quantum Physics II

Covers the concept of matrix to the density operator in quantum physics.