Invariant Theory
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Home > Art, Film & Photography > Invariant Theory: Hilbert's Basis Theorem, Capelli's Identity, Newton's Identities, Polynomial Ring, Littlewood-Richardson Rule
Invariant Theory: Hilbert's Basis Theorem, Capelli's Identity, Newton's Identities, Polynomial Ring, Littlewood-Richardson Rule

Invariant Theory: Hilbert's Basis Theorem, Capelli's Identity, Newton's Identities, Polynomial Ring, Littlewood-Richardson Rule


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 41. Chapters: Hilbert's basis theorem, Capelli's identity, Newton's identities, Polynomial ring, Littlewood-Richardson rule, Ring of symmetric functions, Moduli space, Gr bner basis, Geometric invariant theory, Invariant estimator, Kostant polynomial, Invariant of a binary form, Schur polynomial, Haboush's theorem, Symbolic method, Reynolds operator, Hilbert's fourteenth problem, Chevalley-Shephard-Todd theorem, Differential invariant, Hall algebra, Modular invariant of a group, Molien series, The Classical Groups, Invariants of tensors, Quantum invariant, Cayley's process, Hodge bundle, Catalecticant, Bracket algebra, Transvectant, Hilbert's syzygy theorem, Radical polynomial, Trace identity, Invariant polynomial. Excerpt: In mathematics, Capelli's identity, named after Alfredo Capelli (1887), is an analogue of the formula det(AB) = det(A) det(B), for certain matrices with noncommuting entries, related to the representation theory of the Lie algebra . It can be used to relate an invariant to the invariant, where is Cayley's process. Suppose that xij for i, j = 1, ..., n are commuting variables. Write Eij for the polarization operator The Capelli identity states that the following differential operators, expressed as determinants, are equal: Both sides are differential operators. The determinant on the left has non-commuting entries, and is expanded with all terms preserving their "left to right" order. Such a determinant is often called a column-determinant, since it can be obtained by the column expansion of the determinant starting from the first column. It can be formally written as where in the product first come the elements from the first column, then from the second and so on. The determinant on the far right is Cayley's omega process, and the one on the left is the Capelli determinant. The operators Eij can be wr...


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Product Details
  • ISBN-13: 9781156775714
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 42
  • Spine Width: 2 mm
  • Weight: 95 gr
  • ISBN-10: 115677571X
  • Publisher Date: 29 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Hilbert's Basis Theorem, Capelli's Identity, Newton's Identities, Polynomial Ring, Littlewood-Richardson Rule
  • Width: 189 mm


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