Intuitive Mathematical Economics Series. Linear Structures I. Linear Manifolds, Vector Spaces and Scalar Products
نویسندگان
چکیده
منابع مشابه
Boundedness and Continuity of Fuzzy Linear Order-Homomorphisms on $I$-Topological\ Vector Spaces
In this paper, a new definition of bounded fuzzy linear orderhomomorphism on $I$-topological vector spaces is introduced. Thisdefinition differs from the definition of Fang [The continuity offuzzy linear order-homomorphism. J. Fuzzy Math. {bf5}textbf{(4)}(1997), 829--838]. We show that the ``boundedness"and `` boundedness on each layer" of fuzzy linear orderhomomorphisms do not imply each other...
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Remember that any linear map is fully determined by its action on an (arbitrary) basis. In fact, for ~v = ∑ 1≤k≤n λk~vk one gets νi(~v) = λi ∈ R (i = 1, . . . , n). We prove that ν1, . . . , νn ∈ V ∗ are linearly independent. Assume that the vector α := ∑ 1≤k≤n μkνk ∈ V ∗ is the zero map. I.e. ν(~v) = 0 ∈ R holds for all ~v ∈ V . Since this holds for all ~v ∈ V , it follows that μ1 = μ2 = · · ·...
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In this thesis we introduce a ∆-set Ψ d (R )• which we regard as the piecewise linear analogue of the space Ψd(R ) of smooth d-dimensional submanifolds in R introduced by Galatius in [4]. Using Ψ d (R )• we define a bi-∆-set Cd(R )•,• whose geometric realization BC d (R ) = ∥∥Cd(RN )•,•∥∥ should be interpreted as the PL version of the classifying space of the category of smooth d-dimensional co...
متن کاملSpaces of Piecewise Linear Manifolds
In this thesis we introduce a ∆-set Ψ d (R )• which we regard as the piecewise linear analogue of the space Ψd(R ) of smooth d-dimensional submanifolds in R introduced by Galatius in [4]. Using Ψ d (R )• we define a bi-∆-set Cd(R )•,• whose geometric realization BC d (R ) = ∥∥Cd(RN )•,•∥∥ should be interpreted as the PL version of the classifying space of the category of smooth d-dimensional co...
متن کاملVector Spaces and Linear Transformations
1 Vector spaces A vector space is a nonempty set V , whose objects are called vectors, equipped with two operations, called addition and scalar multiplication: For any two vectors u, v in V and a scalar c, there are unique vectors u + v and cu in V such that the following properties are satisfied. 1. u + v = v + u, 2. (u + v) + w = u + (v + w), 3. There is a vector 0, called the zero vector, su...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2019
ISSN: 1556-5068
DOI: 10.2139/ssrn.3357144