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The sum of the subspaces 6a is the space spanned by the set of all vectors V
such that V belongs to at least one of the ... The vectors V,, V2, • • • , Vr in a vector
space U over 3 are linearly dependent, or constitute a linearly dependent set, ...
spaces over 3, and if t is a bilinear mapping from U, X U2 into '21, then the pair (
31, x) is a tensor product of the vector ... there exists a unique linear
transformation <p from "21 into an arbitrary vector space 3 over 3, such that (px =
a (see 1 32).
a similar sense from the space of all ordered pairs of vectors into the real
numbers between 0 and n. ... Normally the set of scalars is assumed to be a field,
although a comparable theory of vector spaces exists for the case in which the
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This is the 198215th Edition, in two halves, with the Macropaedia and the Micropaedia. First published in 1768, the publisher is the oldest English-language encyclopedia still in print. Two Scottish ... Read full review
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For virtually all its 238 years,Britannica has ruled the shelves as a peerless general encyclopedia. Reviewers have consistently given it high marks for most of the 12 criteria identified inKister's ... Read full review