Definition

A special number that describes how much a vector is stretched or compressed during a transformation, without changing its direction.

Example

In linear algebra, the eigenvalue of a matrix helps determine the behavior of the system it represents.

Conversation

Have you ever heard about the concept of eigenvalue?

Yeah, I think it's related to matrices, right?

Exactly! It's a scalar that helps in understanding linear transformations.

I find it fascinating how it connects different areas of math.

Synonyms & Antonyms

Root Explanation

Eigenvalue → The term 'eigen' comes from the German word 'eigen', meaning 'own' or 'self', and 'value' comes from the Latin 'valere', meaning 'to be strong' or 'to be worth'. The word 'eigenvalue' refers to a value that is characteristic of a particular mathematical object, often associated with its own properties.

Memory Tip

Think of 'eigen' meaning 'own' or 'self' — this helps you remember that an eigenvalue is a value that is intrinsic to a specific mathematical entity.

Visually Confused Words