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@jemoka / Jemoka Knowledge Base / raw/concept/kbhfinite_dimensional_vector_space.md
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--- title: "finite-dimensional vector space" source: https://www.jemoka.com/posts/kbhfinite_dimensional_vector_space/ --- 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’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