Lectures related to Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Symmetric Matrices: Diagonalization

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

Quadratic Forms in IR³

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

Principal Axes Theorem

Explains the Principal Axes Theorem for symmetric matrices and quadratic forms, showing the existence of orthogonal matrices for diagonalization.

Matrices and Quadratic Forms: Key Concepts in Linear Algebra

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, and critical points in functions of two variables.

Diagonalization of Symmetric Matrices

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

Singular Value Decomposition: Applications and Interpretation

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

Quadratic Forms: Definitions, Examples

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

Characteristic Polynomials and Similar Matrices

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

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

Sylvester's Inertia Theorem

Explores Sylvester's Inertia Theorem, relating eigenvalues to diagonal entries in symmetric matrices.

Non-Negative Definite Matrices and Covariance Matrices

Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.

Quadratic Forms and Symmetric Matrices

Explores examples of algebraic quotients using invariance maps and discriminant.

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Linear Algebra: Quadratic Forms and Matrix Diagonalization

Discusses quadratic forms, matrix diagonalization, and their applications in optimization problems.

Diagonalization of Symmetric Matrices

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

Matrix Diagonalization: Spectral Theorem

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