000 08061nam a2200445 i 4500
005 20250919002821.0
008 150324s2014 riua bi 001 0 eng
020 _a9781470409081 (alkaline paper)
_cRM339.43
020 _a1470409089 (alkaline paper)
039 9 _a201506091616
_blan
_c201506050907
_dlan
_c201505271522
_dhamudah
_y03-24-2015
_zhamudah
040 _aDLC
_beng
_erda
_cDLC
_dYDX
_dOCLCO
_dYDXCP
_dCLS
_dIXA
_dDEBBG
_dINU
_dOCLCF
_dUKM
_erda
090 _aQA184.2.D964 2014
090 _aQA184.2
_b.D964 2014
100 1 _aDym, H.
_q(Harry),
_d1938-
245 1 0 _aLinear algebra in action /
_cHarry Dym.
250 _aSecond edition.
264 1 _aProvidence, Rhode Island :
_bAmerican Mathematical Society,
_c[2013].
300 _axix, 585 pages :
_billustrations ;
_c26 cm.
336 _atext
_2rdacontent
337 _aunmediated
_2rdamedia
338 _avolume
_2rdacarrier
490 1 _aGraduate studies in mathematics ;
_vvolume 78.
504 _aIncludes bibliographical references (pages 575-578) and indexes.
505 0 _gMachine generated contents note:
_g1.1.
_tPreview --
_g1.2.
_tThe abstract definition of a vector space --
_g1.3.
_tSome definitions --
_g1.4.
_tMappings --
_g1.5.
_tTriangular matrices --
_g1.6.
_tBlock triangular matrices --
_g1.7.
_tSchur complements --
_g1.8.
_tOther matrix products --
_g2.1.
_tSome preliminary observations --
_g2.2.
_tExamples --
_g2.3.
_tUpper echelon matrices --
_g2.4.
_tThe conservation of dimension --
_g2.5.
_tQuotient spaces --
_g2.6.
_tConservation of dimension for matrices --
_g2.7.
_tFrom U to A --
_g2.8.
_tSquare matrices --
_g3.1.
_tGaussian elimination redux --
_g3.2.
_tProperties of BA and AC --
_g3.3.
_tExtracting a basis --
_g3.4.
_tComputing the coefficients in a basis --
_g3.5.
_tThe Gauss-Seidel method --
_g3.6.
_tBlock Gaussian elimination --
_g3.7.
_t{0, 1, infinity} --
_g3.8.
_tReview --
_g4.1.
_tChange of basis and similarity --
_g4.2.
_tInvariant subspaces --
_g4.3.
_tExistence of eigenvalues --
_g4.4.
_tEigenvalues for matrices --
_g4.5.
_tDirect sums --
_g4.6.
_tDiagonalizable matrices --
_g4.7.
_tAn algorithm for diagonalizing matrices.
505 0 _g4.8.
_tComputing eigenvalues at this point --
_g4.9.
_tNot all matrices are diagonalizable --
_g4.10.
_tThe Jordan decomposition theorem --
_g4.11.
_tAn instructive example --
_g4.12.
_tThe binomial formula --
_g4.13.
_tMore direct sum decompositions --
_g4.14.
_tVerification of Theorem 4.13 --
_g4.15.
_tBibliographical notes --
_g5.1.
_tFunctionals --
_g5.2.
_tDeterminants --
_g5.3.
_tUseful rules for calculating determinants --
_g5.4.
_tEigenvalues --
_g5.5.
_tExploiting block structure --
_g5.6.
_tThe Binet-Cauchy formula --
_g5.7.
_tMinors --
_g5.8.
_tUses of determinants --
_g5.9.
_tCompanion matrices --
_g5.10.
_tCirculants and Vandermonde matrices --
_g6.1.
_tOverview --
_g6.2.
_tStructure of the nullspaces NBj --
_g6.3.
_tChains and cells --
_g6.4.
_tComputing J --
_g6.5.
_tAn algorithm for computing U --
_g6.6.
_tA simple example --
_g6.7.
_tA more elaborate example --
_g6.8.
_tJordan decompositions for real matrices --
_g6.9.
_tProjection matrices --
_g6.10.
_tCompanion and generalized Vandermonde matrices --
_g7.1.
_tFour inequalities --
_g7.2.
_tNormed linear spaces --
_g7.3.
_tEquivalence of norms --
_g7.4.
_tNorms of linear transformations.
505 0 _g7.5.
_tOperator norms for matrices --
_g7.6.
_tMixing tops and bottoms --
_g7.7.
_tEvaluating some operator norms --
_g7.8.
_tInequalities for multiplicative norms --
_g7.9.
_tSmall perturbations --
_g7.10.
_tBounded linear functionals --
_g7.11.
_tExtensions of bounded linear functionals --
_g7.12.
_tBanach spaces --
_g7.13.
_tBibliographical notes --
_g8.1.
_tInner product spaces --
_g8.2.
_tA characterization of inner product spaces --
_g8.3.
_tOrthogonality --
_g8.4.
_tGram matrices --
_g8.5.
_tProjections and direct sum decompositions --
_g8.6.
_tOrthogonal projections --
_g8.7.
_tOrthogonal expansions --
_g8.8.
_tThe Gram-Schmidt method --
_g8.9.
_tToeplitz and Hankel matrices --
_g8.10.
_tAdjoints --
_g8.11.
_tThe Riesz representation theorem --
_g8.12.
_tNormal, selfadjoint and unitary transformations --
_g8.13.
_tAuxiliary formulas --
_g8.14.
_tGaussian quadrature --
_g8.15.
_tBibliographical notes --
_g9.1.
_tHermitian matrices are diagonalizable --
_g9.2.
_tCommuting Hermitian matrices --
_g9.3.
_tReal Hermitian matrices --
_g9.4.
_tProjections and direct sums in Fn --
_g9.5.
_tProjections and rank.
505 0 _g9.6.
_tNormal matrices --
_g9.7.
_tQR factorization --
_g9.8.
_tSchur's theorem --
_g9.9.
_tAreas, volumes and determinants --
_g9.10.
_tBoundary value problems --
_g9.11.
_tBibliographical notes --
_g10.1.
_tSingular value decompositions --
_g10.2.
_tComplex symmetric matrices --
_g10.3.
_tApproximate solutions of linear equations --
_g10.4.
_tFitting a line in R2 --
_g10.5.
_tFitting a line in Rp --
_g10.6.
_tProjection by iteration --
_g10.7.
_tThe Courant-Fischer theorem --
_g10.8.
_tInequalities for singular values --
_g10.9.
_tvon Neumann's inequality for contractive matrices --
_g10.10.
_tBibliographical notes --
_g11.1.
_tPseudoinverses --
_g11.2.
_tThe Moore-Penrose inverse --
_g11.3.
_tBest approximation in terms of Moore-Penrose inverses --
_g11.4.
_tDrazin inverses --
_g11.5.
_tBibliographical notes --
_g12.1.
_tA detour on triangular factorization --
_g12.2.
_tDefinite and semidefinite matrices --
_g12.3.
_tCharacterizations of positive definite matrices --
_g12.4.
_tAn application of factorization --
_g12.5.
_tPositive definite Toeplitz matrices --
_g12.6.
_tDetour on block Toeplitz matrices.
505 0 _g12.7.
_tA maximum entropy matrix completion problem --
_g12.8.
_tA class of A 0 for which (12.52) holds --
_g12.9.
_tSchur complements for semidefinite matrices --
_g12.10.
_tSquare roots --
_g12.11.
_tPolar forms --
_g12.12.
_tMatrix inequalities --
_g12.13.
_tA minimal norm completion problem --
_g12.14.
_tA description of all solutions to the minimal norm completion problem --
_g12.15.
_tBibliographical notes --
_g13.1.
_tSystems of difference equations --
_g13.2.
_tNonhomogeneous systems of difference equations --
_g13.3.
_tThe exponential etA --
_g13.4.
_tSystems of differential equations --
_g13.5.
_tUniqueness --
_g13.6.
_tIsometric and isospectral flows --
_g13.7.
_tSecond-order differential systems --
_g13.8.
_tStability --
_g13.9.
_tNonhomogeneous differential systems --
_g13.10.
_tStrategy for equations --
_g13.11.
_tSecond-order difference equations --
_g13.12.
_tHigher order difference equations --
_g13.13.
_tSecond-order differential equations --
_g13.14.
_tHigher order differential equations --
_g13.15.
_tWronskians --
_g13.16.
_tVariation of parameters --
_g14.1.
_tMean value theorems.
505 0 _g14.2.
_tTaylor's formula with remainder --
_g14.3.
_tApplication of Taylor's formula with remainder --
_g14.4.
_tMean value theorem for functions of several variables --
_g14.5.
_tMean value theorems for vector-valued functions of several variables --
_g14.6.
_tA contractive fixed point theorem --
_g14.7.
_tNewton's method --
_g14.8.
_tA refined contractive fixed point theorem --
_g14.9.
_tSpectral radius --
_g14.10.
_tThe Brouwer fixed point theorem --
_g14.11.
_tBibliographical notes --
_g15.1.
_tPreliminary discussion --
_g15.2.
_tThe implicit function theorem --
_g15.3.
_tA generalization of the implicit function theorem --
_g15.4.
_tContinuous dependence of solutions --
_g15.5.
_tThe inverse function theorem --
_g15.6.
_tRoots of polynomials --
_g15.7.
_tAn instructive example --
_g15.8.
_tA more sophisticated approach --
_g15.9.
_tDynamical systems --
_g15.10.
_tLyapunov functions --
_g15.11.
_tBibliographical notes --
_g16.1.
_tClassical extremal problems --
_g16.2.
_tConvex functions --
_g16.3.
_tExtremal problems with constraints --
_g16.4.
_tExamples --
_g16.5.
_tKrylov subspaces.
650 0 _aAlgebras, Linear.
830 0 _aGraduate studies in mathematics ;
_vvolume 78.
907 _a.b16104201
_b2019-11-12
_c2019-11-12
942 _c01
_n0
_kQA184.2.D964 2014
914 _avtls003581937
990 _arab
991 _aFakulti Sains dan Teknologi
998 _at
_b2015-11-03
_cm
_da
_feng
_griu
_y0
_z.b16104201
999 _c589468
_d589468