Lectures related to Optimal Decision Making: The Simplex Method

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

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Explores the properties of invertible matrices, including unique solutions and linear independence.

Explores diagonalization in 3D linear algebra, covering conditions for diagonalizability and eigenvectors.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

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

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

Explores the properties and examples of diagonalizable matrices, emphasizing the relationship between eigenvectors and eigenvalues.

Covers the Simplex Algorithm, explaining optimality, unbounded costs, and degenerate problems.

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

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

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

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Explores linear algebra concepts through examples and theorems, focusing on matrices and their operations.

Covers LU factorization, linear independence, and matrix equations.

Covers matrix eigenvalues, eigenvectors, and their linear independence.