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Advanced linear algebra and decompositions

#advanced-linear-algebra-and-decompositions · 19 entries. Projects, essays and notes, newest first.

02-02-132Cholesky Decomposition (for PD matrix A)NoteDecompositions: SVD, Cholesky, QR 02-02-133Low-Rank Approximation (truncated SVD)NoteDecompositions: SVD, Cholesky, QR 02-02-134Singular Value DecompositionNoteDecompositions: SVD, Cholesky, QR 02-02-135Characteristic EquationNoteEigenvalues, eigenvectors and the characteristic polynomial 02-02-136Computing Inverse via EigenvectorsNoteEigenvalues, eigenvectors and the characteristic polynomial 02-02-137Eigenvector EquationNoteEigenvalues, eigenvectors and the characteristic polynomial 02-02-138Matrix Expansion EigendecompositionNoteEigenvalues, eigenvectors and the characteristic polynomial 02-02-139Cauchy-Schwarz InequalityNoteInner products and the Gram–Schmidt process 02-02-140Gram-Schmidt (Alternative)NoteInner products and the Gram–Schmidt process 02-02-141Gram-Schmidt (Initialization)NoteInner products and the Gram–Schmidt process 02-02-142Gram-Schmidt (Step k, projection subtraction)NoteInner products and the Gram–Schmidt process 02-02-143Inner Product Axioms (positive definiteness)NoteInner products and the Gram–Schmidt process 02-02-144Orthogonality ConditionNoteInner products and the Gram–Schmidt process 02-02-145Least Squares Solution (underdetermined)NoteLinear transformations and least squares 02-02-146Positive Definite (PD)NoteQuadratic forms and positive definite matrices 02-02-147Positive Semi-Definite (PSD)NoteQuadratic forms and positive definite matrices 02-02-148Regularized Positive DefiniteNoteQuadratic forms and positive definite matrices 02-02-149Kronecker ProductNoteTensor algebra 02-02-150Tensor dot productNoteTensor algebra