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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 9 of 22.

IndexAll notes

02-02-193Euclidean Norm (L₂ norm)Linear algebra and geometryDistance metrics and norms 02-02-194General Metric propertiesLinear algebra and geometryDistance metrics and norms 02-02-195Metric Triangle InequalityLinear algebra and geometryDistance metrics and norms 02-02-196Norm definition constraintLinear algebra and geometryDistance metrics and norms 02-02-197Norm Triangle InequalityLinear algebra and geometryDistance metrics and norms 02-02-198Distance to affine subspaceLinear algebra and geometryOrthogonal projections 02-02-199Normal Equation for general subspace U with basis BLinear algebra and geometryOrthogonal projections 02-02-200Projection error (distance to subspace)Linear algebra and geometryOrthogonal projections 02-02-201Projection matrix onto orthonormal basis BLinear algebra and geometryOrthogonal projections 02-02-202Projection matrix Pπ onto ULinear algebra and geometryOrthogonal projections 02-02-203Projection of x onto 1D subspace (line) U spanned by bLinear algebra and geometryOrthogonal projections 02-02-204Projection of x onto general subspace ULinear algebra and geometryOrthogonal projections 02-02-205Projection onto affine subspace L = x₀ + ULinear algebra and geometryOrthogonal projections 02-02-206Pseudo-inverse of BLinear algebra and geometryOrthogonal projections 02-02-207Rotation about e₁-axisLinear algebra and geometry3D rotations 02-02-208Rotation about e₂-axisLinear algebra and geometry3D rotations 02-02-209Rotation about e₃-axisLinear algebra and geometry3D rotations 02-02-210AdditionLinear algebra and geometryVector operations 02-02-211Cross Product MagnitudeLinear algebra and geometryVector operations 02-02-212Dot ProductLinear algebra and geometryVector operations 02-02-213Linear independenceLinear algebra and geometryVector operations 02-02-214Scalar MultiplicationLinear algebra and geometryVector operations 02-02-215MagnitudeLinear algebra and geometryVector space axioms and coordinates 02-02-216Unit VectorLinear algebra and geometryVector space axioms and coordinates