Glossary math Term Page

Pivot

The leading nonzero entry of a nonzero row

pivot #math#linear-algebra

Korean version

Aliases

pivot

Prerequisites

Matrix

Related Concepts

System of Equations Free Variable Rank Gaussian elimination

Core Idea

A pivot is the first nonzero entry in a nonzero row of an echelon-form matrix. Pivot positions show where independent constraints remain after elimination.

Role In This Blog

In Mathbong, pivots connect Gaussian elimination to rank, free variables, and the classification of solution structures.

Posts Mentioning This Concept

[Linear Algebra Series Part 10] Gaussian Elimination: A Procedure for Solving and Reading Structure Learn Gaussian elimination as both a solving algorithm and a way to expose the structure of a linear system.[선형대수 시리즈 10편] 가우스 소거법: 해를 구하는 절차와 구조 읽기 가우스 소거법을 계산 알고리즘이자 해 구조를 드러내는 도구로 설명합니다.[Linear Algebra Series Part 11] When a System Has One Solution, No Solution, or Infinitely Many Classify the solution structure of a linear system using [[pivot|pivot]]s, [[free-variable|free variables]], and the shape of the reduced system.