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020 _a9780817681944
_9978-0-8176-8194-4
024 7 _a10.1007/978-0-8176-8194-4
_2doi
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_2bicssc
072 7 _aMAT002000
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072 7 _aPBF
_2thema
082 0 4 _a512
100 1 _aKwak, Jin Ho.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLinear Algebra
_h[electronic resource] /
_cby Jin Ho Kwak, Sungpyo Hong.
250 _a2nd ed. 2004.
264 1 _aBoston, MA :
_bBirkhäuser Boston :
_bImprint: Birkhäuser,
_c2004.
300 _aXV, 390 p. 9 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
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505 0 _a1 Linear Equations and Matrices -- 1.1 Systems of linear equations -- 1.2 Gaussian elimination -- 1.3 Sums and scalar multiplications of matrices -- 1.4 Products of matrices -- 1.5 Block matrices -- 1.6 Inverse matrices -- 1.7 Elementary matrices and finding A?1 -- 1.8 LDU factorization -- 1.9 Applications -- 1.10 Exercises -- 2 Determinants -- 2.1 Basic properties of the determinant -- 2.2 Existence and uniqueness of the determinant -- 2.3 Cofactor expansion -- 2.4 Cramer's rule -- 2.5 Applications -- 2.6 Exercises -- 3 Vector Spaces -- 3.1 The n-space ?n and vector spaces -- 3.2 Subspaces -- 3.3 Bases -- 3.4 Dimensions -- 3.5 Row and column spaces -- 3.6 Rank and nullity -- 3.7 Bases for subspaces -- 3.8 Invertibility -- 3.9 Applications -- 3.10 Exercises> -- 4 Linear Transformations -- 4.1 Basic propertiesof linear transformations -- 4.2 Invertiblelinear transformations -- 4.3 Matrices of linear transformations -- 4.4 Vector spaces of linear transformations -- 4.5 Change of bases -- 4.6 Similarity -- 4.7. Applications -- 4.8 Exercises -- 5 Inner Product Spaces -- 5.1 Dot products and inner products -- 5.2 The lengths and angles of vectors -- 5.3 Matrix representations of inner products -- 5.4 Gram-Schmidt orthogonalization -- 5.5 Projections -- 5.6 Orthogonal projections -- 5.7 Relations of fundamental subspaces -- 5.8 Orthogonal matrices and isometries -- 5.9 Applications -- 5.10 Exercises -- 6 Diagonalization -- 6.1 Eigenvalues and eigenvectors -- 6.2 Diagonalization of matrices -- 6.3 Applications -- 6.4 Exponential matrices -- 6.5 Applications continued -- 6.6 Diagonalization of linear transformations -- 6.7 Exercises -- 7 Complex Vector Spaces -- 7.1 The n-space ?n and complex vector spaces -- 7.2 Hermitian and unitary matrices -- 7.3 Unitarily diagonalizable matrices -- 7.4 Normal matrices -- 7.5 Application -- 7.6 Exercises -- 8 Jordan Canonical Forms -- 8.1 Basic properties of Jordan canonical forms -- 8.2 Generalized eigenvectors -- 8.3 The power Ak and the exponential eA -- 8.4 Cayley-Hamilton theorem -- 8.5 The minimal polynomial of a matrix> -- 8.6 Applications -- 8.7 Exercises -- 9 Quadratic Forms -- 9.1 Basic properties of quadratic forms -- 9.2 Diagonalization of quadratic forms -- 9.3 A classification of level surfaces -- 9.4 Characterizations of definite forms -- 9.5 Congruence relation -- 9.6 Bilinear and Hermitian forms -- 9.7 Diagonalization of bilinear or Hermitian forms -- 9.8 Applications -- 9.9 Exercises -- Selected Answers and Hints.
520 _a"A logical development of the subject...all the important theorems and results are discussed in terms of simple worked examples. The student's understanding...is tested by problems at the end of each subsection, and every chapter ends with exercises." --- "Current Science" (Review of the First Edition) A cornerstone of undergraduate mathematics, science, and engineering, this clear and rigorous presentation of the fundamentals of linear algebra is unique in its emphasis and integration of computational skills and mathematical abstractions. The power and utility of this beautiful subject is demonstrated, in particular, in its focus on linear recurrence, difference and differential equations that affect applications in physics, computer science, and economics. Key topics and features include: * Linear equations, matrices, determinants, vector spaces, complex vector spaces, inner products, Jordan canonical forms, and quadratic forms * Rich selection of examples and explanations, as well as a wide range of exercises at the end of every section * Selected answers and hints This second edition includes substantial revisions, new material on minimal polynomials and diagonalization, as well as a variety of new applications. The text will serve theoretical and applied courses and is ideal for self-study. With its important approach to linear algebra as a coherent part of mathematics and as a vital component of the natural and social sciences, "Linear Algebra, Second Edition" will challenge and benefit a broad audience.
650 0 _aAlgebra.
_967
650 0 _aMatrix theory.
650 0 _aComputer science-Mathematics.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 0 _aEconomic theory.
650 1 4 _aAlgebra.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11000
_967
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11094
650 2 4 _aMathematics of Computing.
_0https://scigraph.springernature.com/ontologies/product-market-codes/I17001
650 2 4 _aMath Applications in Computer Science.
_0https://scigraph.springernature.com/ontologies/product-market-codes/I17044
650 2 4 _aMathematical and Computational Engineering.
_0https://scigraph.springernature.com/ontologies/product-market-codes/T11006
650 2 4 _aEconomic Theory/Quantitative Economics/Mathematical Methods.
_0https://scigraph.springernature.com/ontologies/product-market-codes/W29000
700 1 _aHong, Sungpyo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9780817642945
776 0 8 _iPrinted edition:
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856 4 0 _uhttps://s443-doi-org.br.lsproxy.net/10.1007/978-0-8176-8194-4
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