Glossary math Term Page

Homogeneous Equation

A linear equation with zero on the right-hand side

homogeneous-equation #math#linear-algebra

Aliases

homogeneous equation

Prerequisites

System of Equations

Related Concepts

System of Equations Null Space Trivial Solution

Core Idea

A homogeneous equation has the form Ax=0. It always has the trivial solution, and its full solution set is exactly the null space of the matrix.

Role In This Blog

In Mathbong, homogeneous equations tie together independence, null space, free variables, and the structure of solution sets.

Posts Mentioning This Concept

[Linear Algebra Series Part 15] Subspaces, Column Space, and Null Space Use [[subspace|subspace]], [[column-space|column space]], and [[null-space|null space]] to understand what a matrix can produce and what it cannot distinguish.[선형대수 시리즈 15편] 부분공간, 열공간, 영공간 부분공간 개념을 바탕으로 열공간과 영공간을 설명하고, 행렬이 보존하거나 잃는 정보를 해석합니다.