The Real Vector Spaces of Finite Sequences are Finite Dimensional
نویسندگان
چکیده
منابع مشابه
The 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,...
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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...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2009
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-009-0001-2