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goXsqHXP For some mathematical applications, a more abstract approach is sometimes useful. This can be achieved by defining tensors in terms of elements of
tensor products of vector
spaces, which in turn are defined through a universal property.A type (p, q)
tensor is defined in this context as an element of the
tensor product of vector
spaces, ∈ ⊗ ⋯ ⊗ ⏟ ⊗ ∗ ⊗ ⋯ ⊗ ∗ ⏟.
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tielmZHMqhK aRLDrGOQQU WyuskrnOH Ein Banachraum (auch
Banach-Raum, Banachscher Raum) ist in der Mathematik ein vollständiger normierter Vektorraum.Banachräume gehören zu den zentralen Studienobjekten der Funktionalanalysis.Insbesondere sind viele unendlichdimensionale Funktionenräume Banachräume. Sie sind nach dem Mathematiker Stefan
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GDdfqlJPHSU A Schauder basis in a
Banach space X is a sequence {e n} n ≥ 0 of vectors in X with the property that for every vector x in X, there exist uniquely defined scalars {x n} n ≥ 0 depending on x, such that = ∑ = ∞, = (), ():= ∑ =.
Banach spaces with a Schauder basis are necessarily separable, because the countable set of finite linear combinations with rational coefficients (say) is dense. Introduction to Tensor Products of Banach Spaces word download
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QRePymxm hrYPxhVe DEsqVpmrlM (2010-04-23) Independent vectors.Basis of a vector space. The dimension is the largest possible number of independent vectors.. The modern definition of a vector space doesn't involve the concept of dimension which had a towering presence in the historical examples of vector
spaces taken from Euclidean geometry: A line has dimension 1, a plane has dimension 2, "space" has dimension 3, etc.
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