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