Glossary math Term Page

Span

All vectors generated by linear combinations

span #math#linear-algebra

Korean version

Aliases

span

Prerequisites

Vector Linear Combination

Related Concepts

Linear Combination Basis Column Space

Core Idea

The span of a set of vectors is the collection of every vector you can make from their linear combinations. Span is the language of expressibility in linear algebra.

Role In This Blog

In Mathbong, span explains what outputs are reachable, why some systems are solvable, and how basis and column space are built.

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 12] Linear Combinations and Span: What Can These Vectors Produce? Use [[linear-combination|linear combinations]] and [[span|span]] to describe what a vector set can produce and how that connects to [[column-space|column space]].[선형대수 시리즈 12편] 선형결합과 생성 범위(span): 무엇을 만들 수 있는가 선형결합과 생성 범위(span)를 통해 여러 벡터로 만들 수 있는 범위를 이해하고 표현 가능성 관점으로 연결합니다.