Scalar, vector, and matrix mathematics : theory, facts, and formulas|RISS 상세보기

목차 (Table of Contents)

CONTENTS
Preface to the Revised and Expanded Edition = xvii
Preface to the Second Edition = xix
Preface to the First Edition = xxi
Special Symbols = xxv

CONTENTS
Preface to the Revised and Expanded Edition = xvii
Preface to the Second Edition = xix
Preface to the First Edition = xxi
Special Symbols = xxv
Conventions, Notation, and Terminology = xxxvii
1. Sets, Logic, Numbers, Relations, Orderings, Graphs, and Functions = 1
1.1 Sets = 1
1.2 Logic = 2
1.3 Relations and Orderings = 5
1.4 Directed and Symmetric Graphs = 9
1.5 Numbers = 12
1.6 Functions and Their Inverses = 16
1.7 Facts on Logic = 21
1.8 Facts on Sets = 22
1.9 Facts on Graphs = 25
1.10 Facts on Functions = 26
1.11 Facts on Integers = 28
1.12 Facts on Finite Sums = 36
1.13 Facts on Factorials = 49
1.14 Facts on Finite Products = 52
1.15 Facts on Numbers = 52
1.16 Facts on Binomial Coefficients = 54
1.17 Facts on Fibonacci, Lucas, and Pell Numbers = 95
1.18 Facts on Arrangement, Derangement, and Catalan Numbers = 103
1.19 Facts on Cycle, Subset, Eulerian, Bell, and Ordered Bell Numbers = 105
1.20 Facts on Partition Numbers, the Totient Function, and Divisor Sums = 113
1.21 Facts on Convex Functions 116
1.22 Notes = 118
2. Equalities and Inequalities = 119
2.1 Facts on Equalities and Inequalities in One Variable = 119
2.2 Facts on Equalities and Inequalities in Two Variables = 129
2.3 Facts on Equalities and Inequalities in Three Variables = 146
2.4 Facts on Equalities and Inequalities in Four Variables = 177
2.5 Facts on Equalities and Inequalities in Five Variables = 183
2.6 Facts on Equalities and Inequalities in Six Variables = 184
2.7 Facts on Equalities and Inequalities in Seven Variables = 186
2.8 Facts on Equalities and Inequalities in Eight Variables = 187
2.9 Facts on Equalities and Inequalities in Nine Variables = 187
2.10 Facts on Equalities and Inequalities in Sixteen Variables = 187
2.11 Facts on Equalities and Inequalities in n Variables = 188
2.12 Facts on Equalities and Inequalities in 2n Variables = 215
2.13 Facts on Equalities and Inequalities in 3n Variables = 226
2.14 Facts on Equalities and Inequalities in 4n Variables = 226
2.15 Facts on Equalities and Inequalities for the Logarithm Function = 226
2.16 Facts on Equalities for Trigonometric Functions = 231
2.17 Facts on Inequalities for Trigonometric Functions = 246
2.18 Facts on Equalities and Inequalities for Inverse Trigonometric Functions = 254
2.19 Facts on Equalities and Inequalities for Hyperbolic Functions = 261
2.20 Facts on Equalities and Inequalities for Inverse Hyperbolic Functions = 264
2.21 Facts on Equalities and Inequalities in Complex Variables = 266
2.22 Notes = 276
3. Basic Matrix Properties = 277
3.1 Vectors = 277
3.2 Matrices = 280
3.3 Transpose and Inner Product = 285
3.4 Geometrically Defined Sets = 290
3.5 Range and Null Space = 290
3.6 Rank and Defect = 292
3.7 Invertibility = 294
3.8 The Determinant = 299
3.9 Partitioned Matrices = 302
3.10 Majorization = 305
3.11 Facts on One Set = 306
3.12 Facts on Two or More Sets = 310
3.13 Facts on Range, Null Space, Rank, and Defect = 315
3.14 Facts on the Range, Rank, Null Space, and Defect of Partitioned Matrices = 320
3.15 Facts on the Inner Product, Outer Product, Trace, and Matrix Powers = 326
3.16 Facts on the Determinant = 329
3.17 Facts on the Determinant of Partitioned Matrices = 334
3.18 Facts on Left and Right Inverses = 342
3.19 Facts on the Adjugate = 345
3.20 Facts on the Inverse = 348
3.21 Facts on Bordered Matrices = 351
3.22 Facts on the Inverse of Partitioned Matrices = 352
3.23 Facts on Commutators = 354
3.24 Facts on Complex Matrices = 356
3.25 Facts on Majorization = 359
3.26 Notes = 362
4. Matrix Classes and Transformations = 363
4.1 Types of Matrices = 363
4.2 Matrices Related to Graphs = 367
4.3 Lie Algebras = 368
4.4 Abstract Groups = 369
4.5 Addition Groups = 371
4.6 Multiplication Groups = 371
4.7 Matrix Transformations = 373
4.8 Projectors, Idempotent Matrices, and Subspaces = 374
4.9 Facts on Elementary, Group-Invertible, Range-Hermitian, Range-Disjoint, and Range-Spanning Matrices = 376
4.10 Facts on Normal, Hermitian, and Skew-Hermitian Matrices = 377
4.11 Facts on Linear Interpolation = 383
4.12 Facts on the Cross Product = 384
4.13 Facts on Inner, Unitary, and Shifted-Unitary Matrices = 387
4.14 Facts on Rotation Matrices = 391
4.15 Facts on One Idempotent Matrix = 396
4.16 Facts on Two or More Idempotent Matrices = 398
4.17 Facts on One Projector = 407
4.18 Facts on Two or More Projectors = 409
4.19 Facts on Reflectors = 416
4.20 Facts on Involutory Matrices = 417
4.21 Facts on Tripotent Matrices = 417
4.22 Facts on Nilpotent Matrices = 418
4.23 Facts on Hankel and Toeplitz Matrices = 420
4.24 Facts on Tridiagonal Matrices = 422
4.25 Facts on Triangular, Hessenberg, and Irreducible Matrices = 424
4.26 Facts on Matrices Related to Graphs = 426
4.27 Facts on Dissipative, Contractive, Cauchy, and Centrosymmetric Matrices = 427
4.28 Facts on Hamiltonian and Symplectic Matrices = 427
4.29 Facts on Commutators = 428
4.30 Facts on Partial Orderings = 430
4.31 Facts on Groups = 432
4.32 Facts on Quaternions = 437
4.33 Notes = 440
5. Geometry = 441
5.1 Facts on Angles, Lines, and Planes = 441
5.2 Facts on Triangles = 443
5.3 Facts on Polygons and Polyhedra = 489
5.4 Facts on Polytopes = 493
5.5 Facts on Circles, Ellipses, Spheres, and Ellipsoids = 495
6. Polynomial Matrices and Rational Transfer Functions = 499
6.1 Polynomials = 499
6.2 Polynomial Matrices = 501
6.3 The Smith Form and Similarity Invariants = 503
6.4 Eigenvalues = 506
6.5 Eigenvectors = 511
6.6 The Minimal Polynomial = 512
6.7 Rational Transfer Functions and the Smith-McMillan Form = 513
6.8 Facts on Polynomials and Rational Functions = 517
6.9 Facts on the Characteristic and Minimal Polynomials = 524
6.10 Facts on the Spectrum = 530
6.11 Facts on Graphs and Nonnegative Matrices = 537
6.12 Notes = 544
7. Matrix Decompositions = 545
7.1 Smith Decomposition = 545
7.2 Reduced Row Echelon Decomposition = 545
7.3 Multicompanion and Elementary Multicompanion Decompositions = 546
7.4 Jordan Decomposition = 549
7.5 Schur Decomposition = 553
7.6 Singular Value Decomposition, Polar Decomposition, and Full-Rank Factorization = 555
7.7 Eigenstructure Properties = 558
7.8 Pencils and the Kronecker Canonical Form = 563
7.9 Facts on the Inertia = 565
7.10 Facts on Matrix Transformations for One Matrix = 569
7.11 Facts on Matrix Transformations for Two or More Matrices = 575
7.12 Facts on Eigenvalues and Singular Values for One Matrix = 579
7.13 Facts on Eigenvalues and Singular Values for Two or More Matrices = 589
7.14 Facts on Matrix Pencils = 597
7.15 Facts on Eigenstructure for One Matrix = 597
7.16 Facts on Eigenstructure for Two or More Matrices = 603
7.17 Facts on Matrix Factorizations = 605
7.18 Facts on Companion, Vandermonde, Circulant, Permutation, and Hadamard Matrices = 610
7.19 Facts on Simultaneous Transformations = 617
7.20 Facts on Additive Decompositions = 618
7.21 Notes = 619
8. Generalized Inverses = 621
8.1 Moore-Penrose Generalized Inverse = 621
8.2 Drazin Generalized Inverse = 625
8.3 Facts on the Moore-Penrose Generalized Inverse for One Matrix = 628
8.4 Facts on the Moore-Penrose Generalized Inverse for Two or More Matrices = 632
8.5 Facts on the Moore-Penrose Generalized Inverse for Range-Hermitian, Range-Disjoint, and Range-Spanning Matrices = 641
8.6 Facts on the Moore-Penrose Generalized Inverse for Normal Matrices, Hermitian Matrices, and Partial Isometries = 649
8.7 Facts on the Moore-Penrose Generalized Inverse for Idempotent Matrices = 650
8.8 Facts on the Moore-Penrose Generalized Inverse for Projectors = 652
8.9 Facts on the Moore-Penrose Generalized Inverse for Partitioned Matrices = 659
8.10 Facts on the Drazin and Group Generalized Inverses for One Matrix = 669
8.11 Facts on the Drazin and Group Generalized Inverses for Two or More Matrices = 674
8.12 Facts on the Drazin and Group Generalized Inverses for Partitioned Matrices = 678
8.13 Notes = 679
9. Kronecker and Schur Algebra = 681
9.1 Kronecker Product = 681
9.2 Kronecker Sum and Linear Matrix Equations = 683
9.3 Schur Product = 685
9.4 Facts on the Kronecker Product = 685
9.5 Facts on the Kronecker Sum = 691
9.6 Facts on the Schur Product = 697
9.7 Notes = 701
10. Positive-Semidefinite Matrices = 703
10.1 Positive-Semidefinite and Positive-Definite Orderings = 703
10.2 Submatrices and Schur Complements = 704
10.3 Simultaneous Diagonalization = 707
10.4 Eigenvalue Inequalities = 709
10.5 Exponential, Square Root, and Logarithm of Hermitian Matrices = 713
10.6 Matrix Inequalities = 714
10.7 Facts on Range and Rank = 722
10.8 Facts on Unitary Matrices and the Polar Decomposition = 723
10.9 Facts on Structured Positive-Semidefinite Matrices = 724
10.10 Facts on Equalities and Inequalities for One Matrix = 730
10.11 Facts on Equalities and Inequalities for Two or More Matrices = 735
10.12 Facts on Equalities and Inequalities for Partitioned Matrices = 749
10.13 Facts on the Trace for One Matrix = 761
10.14 Facts on the Trace for Two or More Matrices = 763
10.15 Facts on the Determinant for One Matrix = 774
10.16 Facts on the Determinant for Two or More Matrices = 776
10.17 Facts on Convex Sets and Convex Functions = 785
10.18 Facts on Quadratic Forms for One Matrix = 792
10.19 Facts on Quadratic Forms for Two or More Matrices = 795
10.20 Facts on Simultaneous Diagonalization = 799
10.21 Facts on Eigenvalues and Singular Values for One Matrix = 800
10.22 Facts on Eigenvalues and Singular Values for Two or More Matrices = 804
10.23 Facts on Alternative Partial Orderings = 813
10.24 Facts on Generalized Inverses = 815
10.25 Facts on the Kronecker and Schur Products = 820
10.26 Notes = 831
11. Norms = 833
11.1 Vector Norms = 833
11.2 Matrix Norms = 835
11.3 Compatible Norms = 838
11.4 Induced Norms = 841
11.5 Induced Lower Bound = 845
11.6 Singular Value Inequalities = 847
11.7 Facts on Vector Norms = 849
11.8 Facts on Vector p-Norms = 853
11.9 Facts on Matrix Norms for One Matrix = 860
11.10 Facts on Matrix Norms for Two or More Matrices = 868
11.11 Facts on Matrix Norms for Commutators = 884
11.12 Facts on Matrix Norms for Partitioned Matrices = 885
11.13 Facts on Matrix Norms and Eigenvalues for One Matrix = 890
11.14 Facts on Matrix Norms and Eigenvalues for Two or More Matrices = 892
11.15 Facts on Matrix Norms and Singular Values for One Matrix = 895
11.16 Facts on Matrix Norms and Singular Values for Two or More Matrices = 899
11.17 Facts on Linear Equations and Least Squares = 909
11.18 Notes = 912
12. Functions, Limits, Sequences, Series, Infinite Products, and Derivatives = 913
12.1 Open Sets and Closed Sets = 913
12.2 Limits of Sequences = 915
12.3 Series, Power Series, and Bi-power Series = 919
12.4 Continuity = 921
12.5 Derivatives = 924
12.6 Complex-Valued Functions = 926
12.7 Infinite Products = 929
12.8 Functions of a Matrix = 930
12.9 Matrix Square Root and Matrix Sign Functions = 932
12.10 Vector and Matrix Derivatives = 932
12.11 Facts on One Set = 934
12.12 Facts on Two or More Sets = 937
12.13 Facts on Functions = 941
12.14 Facts on Functions of a Complex Variable = 945
12.15 Facts on Functions of a Matrix = 948
12.16 Facts on Derivatives = 949
12.17 Facts on Limits of Functions = 954
12.18 Facts on Limits of Sequences and Series = 957
12.19 Notes = 974
13. Infinite Series, Infinite Products, and Special Functions = 975
13.1 Facts on Series for Subset, Eulerian, Partition, Bell, Ordered Bell, Bernoulli, Euler, and Up/Down Numbers = 975
13.2 Facts on Bernoulli, Euler, Chebyshev, Legendre, Laguerre, Hermite, Bell, Ordered Bell, Harmonic, Fibonacci, and Lucas Polynomials = 981
13.3 Facts on the Zeta, Gamma, Digamma, Generalized Harmonic, Dilogarithm, and Dirichlet L Functions = 994
13.4 Facts on Power Series, Laurent Series, and Partial Fraction Expansions = 1004
13.5 Facts on Series of Rational Functions = 1021
13.6 Facts on Series of Trigonometric and Hyperbolic Functions = 1057
13.7 Facts on Series of Binomial Coefficients = 1063
13.8 Facts on Double-Summation Series = 1071
13.9 Facts on Miscellaneous Series = 1074
13.10 Facts on Infinite Products = 1080
13.11 Notes = 1092
14. Integrals = 1093
14.1 Facts on Indefinite Integrals = 1093
14.2 Facts on Definite Integrals of Rational Functions = 1096
14.3 Facts on Definite Integrals of Radicals = 1111
14.4 Facts on Definite Integrals of Trigonometric Functions = 1114
14.5 Facts on Definite Integrals of Inverse Trigonometric Functions = 1130
14.6 Facts on Definite Integrals of Logarithmic Functions = 1132
14.7 Facts on Definite Integrals of Logarithmic, Trigonometric, and Hyperbolic Functions = 1150
14.8 Facts on Definite Integrals of Exponential Functions = 1157
14.9 Facts on Integral Representations of G and y = 1169
14.10 Facts on Definite Integrals of the Gamma Function = 1171
14.11 Facts on Integral Inequalities = 1171
14.12 Facts on the Gaussian Density = 1172
14.13 Facts on Multiple Integrals = 1173
14.14 Notes = 1178
15. The Matrix Exponential and Stability Theory = 1179
15.1 Definition of the Matrix Exponential = 1179
15.2 Structure of the Matrix Exponential = 1181
15.3 Explicit Expressions = 1185
15.4 Matrix Logarithms = 1187
15.5 Principal Logarithm = 1190
15.6 Lie Groups = 1191
15.7 Linear Time-Varying Differential Equations = 1193
15.8 Lyapunov Stability Theory = 1195
15.9 Linear Stability Theory = 1198
15.10 The Lyapunov Equation = 1201
15.11 Discrete-Time Stability Theory = 1203
15.12 Facts on Matrix Exponential Formulas = 1204
15.13 Facts on the Matrix Sine and Cosine = 1209
15.14 Facts on the Matrix Exponential for One Matrix = 1209
15.15 Facts on the Matrix Exponential for Two or More Matrices = 1211
15.16 Facts on the Matrix Exponential and Eigenvalues, Singular Values, and Norms for One Matrix = 1217
15.17 Facts on the Matrix Exponential and Eigenvalues, Singular Values, and Norms for Two or More Matrices = 1220
15.18 Facts on Stable Polynomials = 1223
15.19 Facts on Stable Matrices = 1226
15.20 Facts on Almost Nonnegative Matrices = 1232
15.21 Facts on Discrete-Time-Stable Polynomials = 1234
15.22 Facts on Discrete-Time-Stable Matrices = 1239
15.23 Facts on Lie Groups = 1243
15.24 Facts on Subspace Decomposition = 1243
15.25 Notes = 1247
16. Linear Systems and Control Theory = 1249
16.1 State Space Models = 1249
16.2 Laplace Transform Analysis and Transfer Functions = 1252
16.3 The Unobservable Subspace and Observability = 1253
16.4 Observable Asymptotic Stability = 1257
16.5 Detectability = 1259
16.6 The Controllable Subspace and Controllability = 1259
16.7 Controllable Asymptotic Stability = 1266
16.8 Stabilizability = 1268
16.9 Realization Theory = 1270
16.10 Zeros = 1278
16.11 H₂System Norm = 1285
16.12 Harmonic Steady-State Response = 1288
16.13 System Interconnections = 1289
16.14 Standard Control Problem = 1291
16.15 Linear-Quadratic Control = 1293
16.16 Solutions of the Riccati Equation = 1295
16.17 The Stabilizing Solution of the Riccati Equation = 1298
16.18 The Maximal Solution of the Riccati Equation = 1302
16.19 Positive-Semidefinite and Positive-Definite Solutions of the Riccati Equation = 1304
16.20 Facts on Linear Differential Equations = 1305
16.21 Facts on Stability, Observability, and Controllability = 1307
16.22 Facts on the Lyapunov Equation and Inertia = 1309
16.23 Facts on the Discrete-Time Lyapunov Equation = 1313
16.24 Facts on Realizations and the H2 System Norm = 1313
16.25 Facts on the Riccati Equation = 1316
16.26 Notes = 1319
Bibliography = 1321
Author Index = 1433
Subject Index = 1449

서점명	서명	판매현황	종이책			전자책 구매링크
서점명	서명	판매현황	정가	판매가(할인율)	포인트(포인트몰)	전자책 구매링크
	Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas - Revised and Expanded Edition	판매중	395,500원	355,950원 (10%)	17,800포인트 (5%)

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