Definition

A special type of vector that, when a specific matrix is applied to it, only gets stretched or shrunk, not rotated. It is associated with a number called an eigenvalue.

Example

In linear algebra, finding the eigenvector of a matrix is essential for understanding its properties.

Conversation

Have you ever heard of an eigenvector?

Yeah, I think it's related to linear transformations, right?

Exactly! It's a vector that doesn't change direction under those transformations.

That's really interesting; I should look into it more!

Synonyms & Antonyms

Root Explanation

Eigenvector is formed from "eigen" (from German, meaning own or self) and "vector" (from Latin "vector", meaning one who carries). The term refers to a vector that is associated with a linear transformation that acts as a scalar multiple of itself, hence it is its own direction or 'own vector'.

Memory Tip

Think of 'eigen' meaning 'own' and 'vector' meaning 'to carry'. An eigenvector is a vector that carries its own direction.

Visually Confused Words