Sylvester's Inertia Theorem

Related lectures (27)

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

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

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

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

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

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

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

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

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