Glossary math Term Page

Null Space

The inputs that a matrix maps to zero

null-space #math#linear-algebra

Korean version

Aliases

null spacekernel

Prerequisites

Vector Subspace

Related Concepts

Subspace Nullity System of Equations

Core Idea

The null space of a matrix is the set of all vectors x satisfying Ax=0. It captures the directions the transformation cannot distinguish because they disappear in the output.

Role In This Blog

In Mathbong, null space explains homogeneous systems, free variables, nullity, information loss, and the structure of non-unique solutions.

Posts Mentioning This Concept

[Linear Algebra Series Part 1] A Linear Algebra Roadmap for Programmers See how this 20-part linear algebra series is sequenced for programming, machine learning, graphics, and data work, and why it is ordered this way.[Linear Algebra Series Part 9] Linear Systems and Ax = b Read a system of linear equations in the form `Ax = b` and interpret it as both a transformation problem and a column-combination problem.[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.