Lectures related to Principal Axes Theorem

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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

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

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

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

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

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

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

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Introduces orthogonal and symmetric matrices in linear algebra with practical examples.

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

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

Delves into singular value decomposition and its applications in linear algebra.

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

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

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

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

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.