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Davis P.J. — Mathematics of Matrices
Davis P.J. — Mathematics of Matrices

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Название: Mathematics of Matrices

Автор: Davis P.J.

Аннотация:

THE use of matrices has now extended beyond mathematics and the physical sciences to business and economics, psychology, and the social and political sciences. The wide use of the first edition of this book confirms the opinion that matrix algebra can and should be introduced to the student as early as possible.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1973

Количество страниц: 366

Добавлена в каталог: 13.04.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel      330
Absolute value      304
Abstract algebra      296
Action of permutation matrices      63
Addition, conformable for      23
Addition, matrix      10 22
Addition, vector      208
Additional problems      313
Algebra, abstract.      296
Algebra, abstract. of determinants      192
Algebra, abstract. of inverses      94
Amplification      253
Analysis, linear      251
Angle geometry      219
Angles in n-space      240
annuities      292
Archimedes      330
Area expansion ratio      201
Area, directed      196
Area, signed      196
Arithmetic progression      280
Associative law of multiplication      45
Associativity, matrix addition      23
Backward substitution      73 77
Barycentric coordinates      235
Bibliography      337
Bilaterial symmetry      307
Binary operation      27
Biographical notices      335
Black Box      245
Bolyai      330
Box, black      245
Box, linear      248
Box, time independent      258
Cantor, George      330
Cayley — Hamilton theorem      267
Cayley, Artur      2 40 336
Center of gravity      239
Change of variable, linear      61
Change of variables      40
Change of variables, quadratic form      65
Characteristic equation      265
Characteristic polynomial      266
Characteristic roots      269
Characteristic values      265
Cofactor      180
Column matrix      4 207
Column vector      4 6
Columns      3
Combination, linear      61
Commutativity, matrix addition      23
Commutativity, matrix addition of matrices      44
Commutativity, of powers      51
Commutator      318
Complex number      296
components of vector      213
Compound interest      292
Conformability conditions      37
Conformable for addition      23
Conformable for multiplication      35
conjugate      304
Continued fractions      284
Contraction      144
Convex sets      232
Coordinates, barycentric      235
Coordinates, homogeneous      168
Correspondences      125
Cotes, Roger      330
Cramer      336
Cramer's rule      205
Cryptography, matrix      331
Cumulative multiplication      34
de l'Hospital      336
De Moivre's theorem      318
De Morgan, A.      337
Degenerate linear, transformations      165
Delay      254
Destruction matrix      258
Determinant      94 171
Determinant expansion      172
Determinant of an inverse      192
Determinants and linear equations      204
Determinants evaluation      183
Determinants, algebra of      192
Determinants, multiplication of      187
Determinants, postulates for      183
Determinants, properties of      176
Device, second order      260
Diagonal elements      4
Diagonal matrix      19
Diagonal matrix, inverse of      88
Diagonal, main      4
Diagonal, main, principal      4
Difference equation, first order linear      287
Difference equation, second order linear      288
Difference equations      280 282
Difference equations, linear simultaneous      284
Difference formula      283
Differencing      254
Differentiation      254
DIMENSION      241
Directed area      196
Direction of vector      214
Distance between two points      214
Distance, Euclidean      240
Distributive laws of multiplication      45
Division algorithm      273
Division of matrix      98
Domain of function      126
Double subscripts      6
Elasticity, theory of      68
Elementary matrices      82
Elementary matrix, inverse of      89
Elementary row transformations      78
Elementary symmetric functions      309
Elements      3
Elements, diagonal      4
Elimination method, Gauss — Jordan      73
Elimination, Gauss — Jordan      99 183
entries      3
Equality of matrices      16
Equation, characteristic      265
Equation, difference      280 282
Equation, linear simultaneous difference      284
Equation, matrix      28
Equation, recurrence      282
Equivalent systems      79
Euclidean distance      240
Euler, Leonard      330
Evaluation, determinants      183
Events      335
expansion      144
Expansion ratio, area      201
Expansion, determinant      172
Exponents, law of      50
Factorial      11 283
Fermat's last theorem      321
Fibonacci numbers      290
Fibonacci, Leonardo      290
Field      299
First order linear difference equation      287
Flexibility matrix      69 121
Formula, difference      283
Fourier, J.B.J.      330
Fractional transformation      328
Free vector      211
Function      125
Function, domain of      126
Function, elementary symmetric      309
Function, identity      127
Function, inverse      128
Function, one to one      127
Function, range of      126
Galileo      131
Galileo transformation      153
Gauss — Jordan elimination      73 99 183
Gauss — Jordan, matrix inversion      99
General inner products      328
Geometric progression      280
Geometrical interpretation, multiplication rule      194
Geometrical vector      207
Geometry of n dimensional space      160
Geometry, angle      219
Gibbs, Josiah Willard      32 336
Goedel, Kurt      330
Graph      12
Grassmann, Hermann      337
Group      308
Groups of matrices      305 310
Groups, theory of      306
Hadamad, Jacques      327
Hadamard matrices      326
Half plane      229
Half spaces      241
Hamilton, William Rowen      2 319 330 336
Heisenberg      2
High powers of matrix      272
Homogeneity      248
Homogeneous coordinates      168
Homogeneous transformations, linear      158
Hooke's law      68 69
Hooke, Robert      68
Householder, A.S.      336
Hyperplane      241
i, j position      6
Idempotent matrix      167 322
Identity function      127
Identity mapping      127
Identity of functions      127
Identity, inverse of      88
Image      133
Image, mirror      142
Imaginary part      296
Incidence matrix      13
Inequality, Schwarz      225
Influence matrices      69 121 323
Influence of coefficients      68 69
Inner product properties      220
Inner products      32 33 207
Inner products of vectors      219
Inner products, general      328
Integration      254
Interest, compound      292
Interpolation      121
Inverse function      128
Inverse mapping      128
Inverse matrix      84
Inverse transformation      128 153
Inverse, of diagonal matrix      88
Inverse, of elementary matrix      89
Inverse, of identity      88
Inverse, of permutation matrix      88
Inverse, of three by three matrix      181
Inverse, of triangular matrix      90
Inverse, of two by two matrix      93
Inverses, algebra of      94
Inversion, matrix      22 83
Isomorphic      303
Iterative method      292
J matrix      19
Jacobi identity      318
Jacobi matrix      317
Klein, Felix      336
Laplace, Pierre Simon      265
Law of exponents      50
Law of superposition      249
Laws of matrix arithmetic, summary      112 113
Leibnitz      336
Lemniscate of Bernoulli      309
Length of vector      213
Lindemann, F.      330
Linear analysis      251
Linear box      248
Linear change of variable      61
linear combination      61
Linear difference equation, first order      287
Linear difference equation, second order      288
Linear equations, simultaneous      57
Linear equations, simultaneous, solution of      72
Linear homogeneous transformations      158
Linear simultaneous difference equations      284
Linear transformation      61 125 132 237
Linear transformations, degenerate      165
Linear transformations, nonhomogeneous      167
Lobatchewski, Nikolai      330
Lorentz transformation      335
Lower triangular matrix      20
m x n matrix      3
Magic square      15 321
Magnitude of vector      213
Main diagonal      4
Mapping      125
Mapping, identity      127
Mapping, inverse      128
Markoff matrix      316
Markoff, Andrey Andreyevitch      316
Mathematical microscope      323
Matrices as operators      245
Matrices as transformations of plane      149
Matrices, column      207
Matrices, commutativity of      44
Matrices, elementary      82
Matrices, equality of      16
Matrices, groups of      305 310
Matrices, Hadamard      326
Matrices, influence      121 323
Matrices, normal      316
Matrices, reduction of      99 105
Matrices, spin      318
Matrix      2
Matrix addition associativity      23
Matrix addition commutativity      23
Matrix arithmetic, summary laws of      112 113
Matrix cryptography      331
Matrix equation      28
Matrix inversion      22 83
Matrix inversion and linear equations      114
Matrix inversion Gauss — Jordan      99
Matrix multiplication      9 22 32 41 43
Matrix polynomial      52
Matrix powers      49
Matrix square roots      313
Matrix subtraction      27
Matrix, column      4
Matrix, destruction      258
Matrix, diagonal      19
Matrix, division by      98
Matrix, flexibility      69 121
Matrix, high powers of      272
Matrix, idempotent      167
Matrix, incidence      13
Matrix, influence      69
Matrix, inverse      84
Matrix, inverse of two by two      93
Matrix, J      19
Matrix, Jacobi      317
Matrix, lower triangular      20
Matrix, m x n      3
Matrix, Markoff      316
Matrix, nonsingular      85
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