Results 1  10
of
147
Basis of Real Linear Space
, 1990
"... this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G ..."
Abstract

Cited by 285 (21 self)
 Add to MetaCart
(Show Context)
this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G
Manyargument relations
 Journal of Formalized Mathematics
, 1990
"... Summary. Definitions of relations based on finite sequences. The arity of relation, the set of logical values Boolean consisting of false and true and the operations of negation and conjunction on them are defined. MML Identifier: MARGREL1. WWW: ..."
Abstract

Cited by 67 (2 self)
 Add to MetaCart
(Show Context)
Summary. Definitions of relations based on finite sequences. The arity of relation, the set of logical values Boolean consisting of false and true and the operations of negation and conjunction on them are defined. MML Identifier: MARGREL1. WWW:
A Theory of Boolean Valued Functions and Partitions, Formalized Mathematics
, 1998
"... ..."
(Show Context)
Linear combinations in real linear space
 Journal of Formalized Mathematics
, 1990
"... Summary. The article is continuation of [17]. At the beginning we prove some theorems concerning sums of finite sequence of vectors. We introduce the following notions: sum of finite subset of vectors, linear combination, carrier of linear combination, linear combination of elements of a given set o ..."
Abstract

Cited by 34 (5 self)
 Add to MetaCart
(Show Context)
Summary. The article is continuation of [17]. At the beginning we prove some theorems concerning sums of finite sequence of vectors. We introduce the following notions: sum of finite subset of vectors, linear combination, carrier of linear combination, linear combination of elements of a given set of vectors, sum of linear combination. We also show that the set of linear combinations is a real linear space. At the end of article we prove some auxiliary theorems that should be proved in [8], [5], [9], [2] or [10].
Interpretation and satisfiability in the first order logic
 Formalized Mathematics
, 1990
"... ..."
(Show Context)
Subcategories and products of categories
 Journal of Formalized Mathematics
, 1990
"... inclusion functor is the injection (inclusion) map E ֒ → which sends each object and each arrow of a Subcategory E of a category C to itself (in C). The inclusion functor is faithful. Full subcategories of C, that is, those subcategories E of C such that HomE(a,b) = HomC(b,b) for any objects a,b of ..."
Abstract

Cited by 29 (1 self)
 Add to MetaCart
(Show Context)
inclusion functor is the injection (inclusion) map E ֒ → which sends each object and each arrow of a Subcategory E of a category C to itself (in C). The inclusion functor is faithful. Full subcategories of C, that is, those subcategories E of C such that HomE(a,b) = HomC(b,b) for any objects a,b of E, are defined. A subcategory E of C is full when the inclusion functor E ֒ → is full. The proposition that a full subcategory is determined by giving the set of objects of a category is proved. The product of two categories B and C is constructed in the usual way. Moreover, some simple facts on bi f unctors (functors from a product category) are proved. The final notions in this article are that of projection functors and product of two functors (complex functors and product functors).
Linear combinations in vector space
 Journal of Formalized Mathematics
, 1990
"... Summary. The notion of linear combination of vectors is introduced as a function from the carrier of a vector space to the carrier of the field. Definition of linear combination of set of vectors is also presented. We define addition and subtraction of combinations and multiplication of combination ..."
Abstract

Cited by 24 (2 self)
 Add to MetaCart
(Show Context)
Summary. The notion of linear combination of vectors is introduced as a function from the carrier of a vector space to the carrier of the field. Definition of linear combination of set of vectors is also presented. We define addition and subtraction of combinations and multiplication of combination by element of the field. Sum of finite set of vectors and sum of linear combination is defined. We prove theorems that belong rather to [6].
Banach space of bounded linear operators
 FORMALIZED MATHEMATICS
, 2003
"... On this article, the basic properties of linear spaces which are defined by the set of all linear operators from one linear space to another are described. Especially, the Banach space is introduced. This is defined by the set of all bounded linear operators. ..."
Abstract

Cited by 23 (19 self)
 Add to MetaCart
(Show Context)
On this article, the basic properties of linear spaces which are defined by the set of all linear operators from one linear space to another are described. Especially, the Banach space is introduced. This is defined by the set of all bounded linear operators.