Linear-Algebra on The Standard Errorhttps://jongha-jeon-dev.github.io/standarderror/tags/linear-algebra/Recent content in Linear-Algebra on The Standard ErrorHugo -- 0.123.7en-gbTue, 01 Sep 2026 00:00:00 +0000Linear Algebra 1: The Condition Number Is the Error Bar on Your Solvehttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-1-condition-number/Thu, 27 Aug 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-1-condition-number/A 14 by 14 system whose answer is all ones, solved to a residual at machine precision, returning entries between -4.9 and +8.5 — and the one number on the matrix that predicts it.Linear Algebra 2: Least Squares Three Ways, and Only Two Survivehttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-2-least-squares-three-ways/Thu, 27 Aug 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-2-least-squares-three-ways/The closed form in every regression textbook is a correct formula and a bad algorithm. On exact data it returns coefficients wrong by 14 percent where two other routes get ten decimal places.Linear Algebra 3: Your Covariance Matrix Is Not Positive Definitehttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-3-positive-definite/Thu, 27 Aug 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-3-positive-definite/Three correlations, each one a defensible estimate, each one inside [-1, 1] — and together a claim that a particular portfolio has a variance of minus 0.11.Linear Algebra 4: PCA When Two Eigenvalues Are Equalhttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-4-equal-eigenvalues/Mon, 31 Aug 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-4-equal-eigenvalues/A correlation matrix whose two largest eigenvalues differ by 0.02, where the component carrying the most variance is the one that moves 42 degrees between samples — and the resampling check reports a third of it.Linear Algebra 5: What Ridge Does to the Geometryhttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-5-ridge-geometry/Tue, 01 Sep 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-5-ridge-geometry/Every variance inflation factor at 1.00 on a design with a condition number near a billion, a cross-validated ridge fit that spends 3.6 of its 9 parameters, and a nominal 95 percent interval that covers 34 percent.Linear Algebra 6: One Row Can Own the Fithttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-6-one-row/Tue, 01 Sep 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-6-one-row/A single observation with a residual of exactly zero, a Cook's distance of 0/0, and a coefficient that stops existing when you delete it — and, separately, one row moving a slope by six standard errors.Linear Algebra 7: The Scree Plot Lieshttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-7-scree-plot/Tue, 01 Sep 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-7-scree-plot/Asked about a matrix of pure noise, the elbow returns 18 different answers across 300 draws and never once returns none — while three calibrated rules get it right. And the rule that is provably optimal reports zero components where three exist.Linear Algebra 8: When There Is No Closed Formhttps://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-8-no-closed-form/Tue, 01 Sep 2026 00:00:00 +0000https://jongha-jeon-dev.github.io/standarderror/lectures/linear-algebra-8-no-closed-form/A logistic regression where one coefficient's value is the iteration limit, its standard error is a constant the library author chose, and its p-value crosses 0.05 on the way down — while every other coefficient in the table is correct to three decimal places.