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Home > Art, Film & Photography > Bilinear Forms: Inner Product Space, Covariance, Dot Product, Symplectic Vector Space, Bilinear Form, Symmetric Bilinear Form, Degenerate Form
Bilinear Forms: Inner Product Space, Covariance, Dot Product, Symplectic Vector Space, Bilinear Form, Symmetric Bilinear Form, Degenerate Form

Bilinear Forms: Inner Product Space, Covariance, Dot Product, Symplectic Vector Space, Bilinear Form, Symmetric Bilinear Form, Degenerate Form


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Inner Product Space, Covariance, Dot Product, Symplectic Vector Space, Bilinear Form, Symmetric Bilinear Form, Degenerate Form, Isotropic Quadratic Form, Cartan-dieudonn Theorem, Unimodular Form. Excerpt: In mathematics, an inner product space is a vector space with the additional structure called an inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the length of a vector or the angle between two vectors. They also provide the means of defining orthogonality between vectors (zero inner product). Inner product spaces generalize Euclidean spaces (in which the inner product is the dot product, also known as the scalar product) to vector spaces of any (possibly infinite) dimension, and are studied in functional analysis. An inner product space is sometimes also called a pre-Hilbert space, since its completion with respect to the metric, induced by its inner product, is a Hilbert space. That is, if a pre-Hilbert space is complete with respect to the metric arising from its inner product (and norm), then it is called a Hilbert space. Inner product spaces were referred to as unitary spaces in earlier work, although this terminology is now rarely used. In this article, the field of scalars denoted is either the field of real numbers or the field of complex numbers . Formally, an inner product space is a vector space V over the field together with an inner product, i.e., with a map that satisfies the following three axioms for all vectors and all scalars: with equality only for Notice that conjugate symmetry implies that is real for all, since we have Conjugate ... More: http: //booksllc.net/?id=14856


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Product Details
  • ISBN-13: 9781156823798
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 58
  • Spine Width: 3 mm
  • Weight: 95 gr
  • ISBN-10: 115682379X
  • Publisher Date: 24 May 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Inner Product Space, Covariance, Dot Product, Symplectic Vector Space, Bilinear Form, Symmetric Bilinear Form, Degenerate Form
  • Width: 229 mm


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