Glossary math Term Page

Rank

The number of independent output directions

rank #math#linear-algebra

Korean version

Aliases

rank

Prerequisites

Column Space Dimension

Related Concepts

Column Space Nullity Basis

Core Idea

Rank is the dimension of the column space, or equivalently the maximum number of linearly independent columns of a matrix. It measures how much distinct output structure the matrix can preserve.

Role In This Blog

In Mathbong, rank is used to interpret solvability, invertibility, pivots, information preservation, and low-rank approximation.

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 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.