000 03474nam a22005415i 4500
001 978-1-4020-5495-2
003 DE-He213
005 20161121231126.0
007 cr nn 008mamaa
008 100301s2007 ne | s |||| 0|eng d
020 _a9781402054952
_9978-1-4020-5495-2
024 7 _a10.1007/978-1-4020-5495-2
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
082 0 4 _a512
_223
100 1 _aGolan, Jonathan S.
_eauthor.
245 1 4 _aThe Linear Algebra a Beginning Graduate Student Ought to Know
_h[electronic resource] /
_cby Jonathan S. Golan.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2007.
300 _aXII, 436 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aNotation and terminology -- Fields -- Vector spaces over a field -- Algebras over a field -- Linear independence and dimension -- Linear transformations -- The endomorphism algebra of a vector space -- Representation of linear transformations by matrices -- The algebra of square matrices -- Systems of linear equations -- Determinants -- Eigenvalues and eigenvectors -- Krylov subspaces -- The dual space -- Inner product spaces -- Orthogonality -- Selfadjoint Endomorphisms -- Unitary and Normal endomorphisms -- Moore-Penrose pseudoinverses -- Bilinear transformations and forms.
520 _aLinear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. The book is intended to be used in one of several possible ways: (1) as a self-study guide; (2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or (3) as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.
650 0 _aMathematics.
650 0 _aNumerical analysis.
650 0 _aAlgebra.
650 0 _aAssociative rings.
650 0 _aRings (Algebra).
650 0 _aMatrix theory.
650 0 _aNonassociative rings.
650 0 _aAlgorithms.
650 1 4 _aMathematics.
650 2 4 _aAlgebra.
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
650 2 4 _aAssociative Rings and Algebras.
650 2 4 _aNon-associative Rings and Algebras.
650 2 4 _aNumeric Computing.
650 2 4 _aAlgorithms.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781402054945
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4020-5495-2
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c508977
_d508977