منابع مشابه
Inner Product Spaces and Orthogonality
1 Dot product of R The inner product or dot product of R is a function 〈 , 〉 defined by 〈u,v〉 = a1b1 + a2b2 + · · ·+ anbn for u = [a1, a2, . . . , an] , v = [b1, b2, . . . , bn] ∈ R. The inner product 〈 , 〉 satisfies the following properties: (1) Linearity: 〈au + bv,w〉 = a〈u,w〉+ b〈v,w〉. (2) Symmetric Property: 〈u,v〉 = 〈v,u〉. (3) Positive Definite Property: For any u ∈ V , 〈u,u〉 ≥ 0; and 〈u,u〉 =...
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The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately represented in terms of the notion of measure cone and the mixing distance [1], a specification of the novel concept of direction distance [2]. It turns out tha...
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The notion of frame in a Banach spaces E via semi-inner product was introduced and studied in [16]. In this paper, we give a characterisation for SIP-II Ed-Bessel sequence to be SIP-II Ed-frame. Also, a necessary and sufficient condition for the finite sum of SIP-II Ed frame for E to be a SIP-II Ed frame for E has been obtained. Further, a sufficient condition for the stability of finite sum of...
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ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 1981
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496159314