---
title: "finite-dimensional vector space"
type: concept
related: [Vector Space, Finite Dimensional Vector Space, Basis]
source: https://www.jemoka.com/posts/kbhfinite_dimensional_vector_space/
confidence: high
status: active
---

A finite-dimensional vector space is a vector space where some actual list (which remember, has finite length) of vectors spans the space.
An infinite-demensional vector space is a vector space that&rsquo;s not a finite-dimensional vector space.
additional information every finite-dimensional vector space has a basis Begin with a spanning list in the finite-dimensional vector space you are working with. Apply the fact that all spanning lists contains a basis of which you are spanning. Therefore, some elements of that list form a basis of the finite-dimensional vector space you are working with. \(\blacksquare\)
finite-dimensional subspaces finite-dimensional subspaces
