Glossary math Term Page

Normal Equation

The equation encoding the least-squares condition

normal-equation #math#linear-algebra

Korean version

Aliases

normal equation

Prerequisites

Dot Product Least Squares

Related Concepts

Least Squares Residual Linear Regression Projection

Core Idea

The normal equation is the algebraic form of the least-squares condition. The standard expression A^T A x = A^T b comes from requiring the residual to be orthogonal to the column space of A.

Role In This Blog

In Mathbong, the normal equation serves as the algebraic bridge between projection geometry and linear regression fitting.

Posts Mentioning This Concept

[Linear Algebra Series Part 18] Least Squares and the Basics of Linear Regression Use [[least-squares|least squares]] and [[linear-regression|linear regression]] to find the best approximate solution when `Ax = b` has no exact answer.[선형대수 시리즈 18편] 최소제곱과 선형회귀의 기초 해가 정확히 맞지 않는 선형시스템에서 최소제곱 해를 구하는 아이디어를 선형회귀와 연결합니다.