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02-02Notes

A working library of the mathematics behind the analysis.

524 notes in 7 areas, from notation to machine learning. Each takes one formula: what it says, a small worked example, and code that runs. Revised in place. Page 6 of 22.

IndexAll notes

02-02-121Nested radicalsAlgebra and precalculusRoots and radicals 02-02-122Power of radicalAlgebra and precalculusRoots and radicals 02-02-123Addition/Subtraction RuleAlgebra and precalculusLimits 02-02-124Division ruleAlgebra and precalculusLimits 02-02-125Multiplication ruleAlgebra and precalculusLimits 02-02-126Constant extractionAlgebra and precalculusSummations 02-02-127Distribution over additionAlgebra and precalculusSummations 02-02-128Exponentiation of a sumAlgebra and precalculusSummations 02-02-129Index shiftingAlgebra and precalculusSummations 02-02-130Splitting sumsAlgebra and precalculusSummations 02-02-131Sum of a product (log)Algebra and precalculusSummations 02-02-132Cholesky Decomposition (for PD matrix A)Linear algebra and geometryDecompositions: SVD, Cholesky, QR 02-02-133Low-Rank Approximation (truncated SVD)Linear algebra and geometryDecompositions: SVD, Cholesky, QR 02-02-134Singular Value DecompositionLinear algebra and geometryDecompositions: SVD, Cholesky, QR 02-02-135Characteristic EquationLinear algebra and geometryEigenvalues, eigenvectors and the characteristic polynomial 02-02-136Computing Inverse via EigenvectorsLinear algebra and geometryEigenvalues, eigenvectors and the characteristic polynomial 02-02-137Eigenvector EquationLinear algebra and geometryEigenvalues, eigenvectors and the characteristic polynomial 02-02-138Matrix Expansion EigendecompositionLinear algebra and geometryEigenvalues, eigenvectors and the characteristic polynomial 02-02-139Cauchy-Schwarz InequalityLinear algebra and geometryInner products and the Gram–Schmidt process 02-02-140Gram-Schmidt (Alternative)Linear algebra and geometryInner products and the Gram–Schmidt process 02-02-141Gram-Schmidt (Initialization)Linear algebra and geometryInner products and the Gram–Schmidt process 02-02-142Gram-Schmidt (Step k, projection subtraction)Linear algebra and geometryInner products and the Gram–Schmidt process 02-02-143Inner Product Axioms (positive definiteness)Linear algebra and geometryInner products and the Gram–Schmidt process 02-02-144Orthogonality ConditionLinear algebra and geometryInner products and the Gram–Schmidt process