General Linear Model: Symmetric Matrices

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

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

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

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

Explores linear models, least squares, Gaussian vectors, and model selection methods.

Explores nested model selection in linear models, comparing models through sums of squares and ANOVA, with practical examples.

Explores the dangers of multicollinearity in linear models and discusses diagnostic methods and remedies.

Discusses the geometry of least squares, exploring row and column perspectives, hyperplanes, projections, residuals, and unique vectors.

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.