On a Characterization of Finite-Dimensional Vector Spaces
نویسندگان
چکیده
We provide a characterization of the finite dimensionality vector spaces in terms right-sided invertibility linear operators on them.
منابع مشابه
Vector Spaces II : Finite Dimensional Linear Algebra
Example 3. If X ⊆ RN is a vector space then it is a vector subspace of RN . Example 4. R1 is a vector subspace of R2. But the set [−1, 1] is not a vector subspace because it is not closed under either vector addition or scalar multiplication (for example, 1 + 1 = 2 6∈ [−1, 1]). Geometrically, a vector space in RN looks like a line, plane, or higher dimensional analog thereof, through the origin...
متن کاملThe Real Vector Spaces of Finite Sequences are Finite Dimensional
In this paper we show the finite dimensionality of real linear spaces with their carriers equal R n. We also give the standard basis of such spaces. For the set R n we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n. We use the following convention: i, j, n are elements of N, z, B 0 are sets,...
متن کاملA‰ne line systems in finite-dimensional vector spaces
A topological translation plane may be defined as a system L of a‰ne l-dimensional subspaces of R such that (1) any two points are joined by a unique line L A L and joining is continuous; (2) Euclid’s parallel postulate holds and L is invariant under translation. It is easy to see that one of the two parts of condition (2) may be omitted. We use topological methods to show that (2) may be omitt...
متن کاملA Simple Metric for Finite Dimensional Vector Spaces
A new metric for subspaces of a finite dimensional vector space V is identified. The metric is determined by the dimensions of M + N and M∩N , where M and N are subspaces of V . Some properties of the metric are derived as well. 2000 Mathematics Subject Classification: 15A03
متن کاملOn Partitions of Finite vector Spaces
In this note, we give a new necessary condition for the existence of non-trivial partitions of a finite vector space. Precisely, we prove that the number of the subspaces of minimum dimension t of a non-trivial partition of Vn(q) is greater than or equal to q + t. Moreover, we give some extensions of a well known Beutelspacher-Heden’s result on existence of T -partitions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2021
ISSN: ['1687-0425', '0161-1712']
DOI: https://doi.org/10.1155/2021/8895949