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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 7 of 22.

IndexAll notes

02-02-145Least Squares Solution (underdetermined)Linear algebra and geometryLinear transformations and least squares 02-02-146Positive Definite (PD)Linear algebra and geometryQuadratic forms and positive definite matrices 02-02-147Positive Semi-Definite (PSD)Linear algebra and geometryQuadratic forms and positive definite matrices 02-02-148Regularized Positive DefiniteLinear algebra and geometryQuadratic forms and positive definite matrices 02-02-149Kronecker ProductLinear algebra and geometryTensor algebra 02-02-150Tensor dot productLinear algebra and geometryTensor algebra 02-02-151Matrix additionLinear algebra and geometryBasic principles and operations 02-02-152Matrix definitionLinear algebra and geometryBasic principles and operations 02-02-153Matrix multiplicationLinear algebra and geometryBasic principles and operations 02-02-154Scalar multiplicationLinear algebra and geometryBasic principles and operations 02-02-155Trace DefinitionLinear algebra and geometryBasic principles and operations 02-02-156TransposeLinear algebra and geometryBasic principles and operations 02-02-157Condition Number (matrix conditioning)Linear algebra and geometryDeterminants and inverses 02-02-158Determinant (2×2)Linear algebra and geometryDeterminants and inverses 02-02-159Determinant Identity (eigenvalues)Linear algebra and geometryDeterminants and inverses 02-02-160Identity matrix determinantLinear algebra and geometryDeterminants and inverses 02-02-161Inverse determinantLinear algebra and geometryDeterminants and inverses 02-02-162Inverse matrix (2×2)Linear algebra and geometryDeterminants and inverses 02-02-163Product determinantLinear algebra and geometryDeterminants and inverses 02-02-164Systems of Linear EquationsLinear algebra and geometryDeterminants and inverses 02-02-165Trace Identity (eigenvalues)Linear algebra and geometryDeterminants and inverses 02-02-166Transpose determinantLinear algebra and geometryDeterminants and inverses 02-02-167Chebyshev Distance (L∞ norm, p → ∞)Linear algebra and geometryAdvanced distance and similarity metrics 02-02-168Cosine DistanceLinear algebra and geometryAdvanced distance and similarity metrics