Advanced Analysis II: Local Extrema and Hessians

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Explores the diagonalization of symmetric matrices using eigenvectors and eigenvalues, emphasizing orthogonality and real eigenvalues.

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

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

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

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

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

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

Covers matrix multiplication, properties, and inverses in linear algebra.

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

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