Primary
Linear Independence ○｜Definition｜1st｜20251119205401-00-⌔
Linear independence - Wikipedia
Linear independence
In linear algebra, a set of vectors is said to be linearly independent if there exists no vector in the set that is equal to a linear combination of the other vectors in the set. If such a vector exists, then the vectors are said to be linearly dependent. Linear independence is part of the definition of linear basis.1
A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
Printed 2026-06-28.
(echo:: @ ᯤ)
Link to original Footnotes
G. E. Shilov, Linear Algebra (Trans. R. A. Silverman), Dover Publications, New York, 1977. ↩
Secondary
• • •