Lectures related to Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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

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

Principal Axes Theorem

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

Quadratic Forms in IR³

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

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.

Linear Algebra: Quadratic Forms and Matrix Diagonalization

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

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Diagonalization of Symmetric Matrices

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

Sylvester's Inertia Theorem

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

Inertia Tensor: Main Axes and Principal Moments

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Spectral Theorem Recap

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

Singular Value Decomposition: Applications and Interpretation

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

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Symmetric Matrices and Quadratic Forms

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

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Matrix Decomposition: Triangular and Spectral

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

Spectral Decomposition of Symmetric Matrices

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

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices and the importance of Singular Value Decomposition.