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Background and purpose: Chronic carotid artery occlusion remains a poorly understood risk factor for subsequent stroke, and potential revascularization is dependent on understanding the anatomy and nature of the occlusion. Luminal imaging cannot assess the nature of an occlusion, so the internal structure of the occlusion must be inferred.
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Daha fazla öğreninThis is a k -linear category: that is, it's enriched over v e c t k - or equivalently, in simpler terms, the hom-sets are vector spaces over k and composition is bilinear. But I don't think it's a module category over v e c t k, since you can't tensor a 7-dimensional vector space by an arbitrary vector space and get another 7-dimensional …
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Daha fazla öğreninGlenn K Klute 1, Brian C Glaister, Jocelyn S Berge. Affiliation 1 Department of Veterans Affairs, RR&D Center of Excellence, Seattle, WA 98108, USA. [email protected]; PMID: 20384553 DOI: 10.3109/03093641003645528 Abstract Prosthetic liners exist to improve amputee safety and comfort by adding a cushioning layer between the residual …
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Daha fazla öğreninSolution. First, we have just seen that T(→v) = proj→u(→v) is linear. Therefore by Theorem 5.2.1, we can find a matrix A such that T(→x) = A→x. The columns of the matrix for T are defined above as T(→ei). It follows that T(→ei) = proj→u(→ei) gives the ith column of the desired matrix.
Daha fazla öğreninlinear maps. 1. Vector spaces Suppose k is a field. (Although the theory works for arbitrary fields, we will eventually focus only on the choices k = R,C.) Definition. A k-vector space is an abelian group (V,+), equipped with an external operation1 k ×V 3(λ,v) 7−→λv ∈V, called scalar multiplication, with the following properties:
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