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Parham Salehyan
Hasse-Schmidt Derivations on Grassmann Algebras
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2641580Hasse-Schmidt Derivations on Grassmann Algebrashttps://www.gandhi.com.mx/hasse-schmidt-derivations-on-grassmann-algebras-9783319318424/phttps://gandhi.vtexassets.com/arquivos/ids/3333525/af947f7e-ad5a-4a86-8887-eeb6b86022ae.jpg?v=63838522340100000021472385MXNSpringer International PublishingInStock/Ebooks/<p>This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzers method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambellis formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.</p>...2577740Hasse-Schmidt Derivations on Grassmann Algebras21472385https://www.gandhi.com.mx/hasse-schmidt-derivations-on-grassmann-algebras-9783319318424/phttps://gandhi.vtexassets.com/arquivos/ids/3333525/af947f7e-ad5a-4a86-8887-eeb6b86022ae.jpg?v=638385223401000000InStockMXN99999DIEbook20169783319318424_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_<p>This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzers method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambellis formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.</p>(*_*)9783319318424_<p>This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzers method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambellis formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.</p>...9783319318424_Springer International Publishinglibro_electonico_74732f03-3a35-3fc3-b5fe-2ae778b1051c_9783319318424;9783319318424_9783319318424Parham SalehyanInglésMéxico2016-07-08T00:00:00+00:00Springer International Publishing