Lectures related to Composite Materials: Implementation Principles

Characteristic Polynomials and Similar Matrices

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

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Optimal Decision Making: The Simplex Method

Introduces the Simplex Method for optimal decision making in linear programming, covering basic and advanced concepts.

Spectral Decomposition of Symmetric Matrices

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

Matrix Similarity and Diagonalization

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

Diagonalizability of Matrices

Explores the diagonalizability of matrices through eigenvectors and eigenvalues, emphasizing their importance and practical implications.

Diagonalization: Criteria and Examples

Covers the criteria for diagonalizing a matrix and provides illustrative examples.

Orthogonal Base Change

Explores orthogonal base change in linear algebra, focusing on matrices and transformations.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Natural Cubic Splines

Explains the construction of natural cubic splines, emphasizing smoothness and continuity in the function representation.

Matrix Decomposition: Triangular and Spectral

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Eigenvalues and Similar Matrices

Explores eigenvalues, matrix trace, and similarity, highlighting their significance in matrix properties.

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.

The Simplex Algorithm

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

Matrix Reduction: Part 1

Covers the reduction of a linear transformation in a 2-dimensional space to find a simpler matrix representation.

Linear Algebra Basics: Vector Spaces, Transformations, Eigenvalues

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Singular Value Decomposition: Applications and Interpretation

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

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.