Glossary math Term Page

Eigenvector

A direction preserved by a transformation

eigenvector #math#linear-algebra

Korean version

Aliases

eigenvector

Prerequisites

Matrix Linear Transformation

Related Concepts

Eigenvalue Basis Matrix

Core Idea

An eigenvector is a nonzero vector that stays on the same line after a linear transformation is applied. Its direction is special because the transformation changes only its scale, not its subspace.

Role In This Blog

In Mathbong, eigenvectors are the special axes that make diagonalization, PCA, and matrix interpretation much clearer.

Posts Mentioning This Concept

[Linear Algebra Series Part 19] Eigenvalues and Eigenvectors: Directions That Stay Special Under a Transformation Use [[eigenvalue|eigenvalues]] and [[eigenvector|eigenvectors]] to understand special directions of a transformation and connect them to [[pca|PCA]].[선형대수 시리즈 19편] 고유값과 고유벡터: 변환 속에서 유지되는 축 고유값과 고유벡터를 반복 변환에서 유지되는 방향과 크기 변화로 설명하고 주성분 분석(PCA) 직관과 연결합니다.