Glossary math Term Page

Linear Combination

A sum of scaled vectors

linear-combination #math#linear-algebra

Korean version

Aliases

linear combination

Prerequisites

Vector Scalar

Related Concepts

Vector Span Basis

Core Idea

A linear combination is built by multiplying vectors by scalars and then adding them. It is the most basic way linear algebra answers the question: what can these vectors produce together?

Role In This Blog

In Mathbong, linear combinations lead directly to span, column space, basis, and the interpretation of Ax as a combination of matrix columns.

Posts Mentioning This Concept

[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.