Glossary math Term Page

Column Space

The output space of a matrix

column-space #math#linear-algebra

Aliases

column space

Prerequisites

Related Concepts

Span Subspace Rank

Core Idea

The column space of a matrix is the set of all vectors of the form Ax. Equivalently, it is the span of the matrix columns.

Role In This Blog

In Mathbong, column space is the answer to what a matrix can produce, and it appears in solvability, rank, projection, and least squares.

Posts Mentioning This Concept

[Linear Algebra Series Part 7] What Does Matrix-Vector Multiplication Actually Do? Understand matrix-vector multiplication as both row-wise computation and a column combination, then connect it to linear layers and output spaces.[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 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.