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Nicholson W.K. — Linear Algebra with Applications
Nicholson W.K. — Linear Algebra with Applications

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Название: Linear Algebra with Applications

Автор: Nicholson W.K.

Аннотация:

This manual contains answers and solutions to selected problems from this text. This easy-to-use, symbolic algebra and graphing package for the Macintosh emphasizes visual, interactive problem-solving. These electronic problem sets, which are in addition to those in the text, are for use with the Macintosh.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third Edition

Год издания: 1995

Количество страниц: 540

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value of a complex number      467
Adjoint matrix      108 123
Adjoint matrix, formula for inverse      125
Al — Khowarizmi      475
Algorithm, Cholesky      291
Algorithm, diagonalization      262
Algorithm, Gaussian      12 17
Algorithm, Gram — Schmidt      275 434
Algorithm, matrix inversion      61
Algorithm, QR — Algorithm      300
Algorithm, simplex      496
Algorithm, tnangulatron      404
angle      156 431
Angle, between two vectors      431
Angle, cosine of      469
Angle, radian measure      469
Angle, sine ot      469
Angle, standard position      469
Approximation, best      325
Approximation, Fourier      462
Approximation, least squares      178 327
Approximation, theorem      438
Argument of a complcx number      470
Associated homogeneous      50
Back substitution      19 79
Basis      213
Basis of eigenvectors      262 441 445
Basis, existence of      221
Basis, ordered      371
Basis, orthogonal      273 433
Basis, standard      214 303
Bessel’s inequality      441
Best approximation theorem      325
Bilinear form      324
Binet formula      416
Binomial coefficients      243
Binomial coefficients, theorem      243
Block, diagonal matnx      67
Block, multiplication      52
Block, partition of a matrix      52
Block, triangular matnx      78 391
Block, triangulation theorem      402
Brown.J W      461
Cancellation for matnx muliiplication      64
Cancellation for vector addition      191
Cauchy inequaliiy      428
Cauchy — Schwarz inequality      165
Cauchy, A I.      428
Cayley — Hamilton theorem      407
Cayley. A      33 407
Centroid of a triangle      155
Change of basis matrix      380
Characteristic polynomial      253 306
Characteristic polynomial of a block triangular matrix      391
Characteristic polynomial of a differential equation      245
Characteristic polynomial of an operator      186
Characteristic value      251
Characteristic value, vector      251
Cholesky decomposition      290
Cholesky decomposition, algorithm      291
Churchill, R V      463
Circuit rule      29
Closed economy      91
Coefficient matnx      5 50
Coefficients of an equation of a linear combination      204
Coefficients of an equation of a polynomial      191
Column matnx      34
Column space      228
Commute      45
Companion matnx      120
Complcx linear algebra      302—310
Complcx plane      468
Complement of a subspace      395
Completing the square      475
Complex distance formula      468
Complex matnx      304
Complex number      465
Complex number, absolute value      467
Complex number, argument      470
Complex number, conjugate      467
Complex number, DeMoivre’s theorem      472
Complex number, fundamental theorem of algebra      477
Complex number, imaginary part      465
Complex number, inverse of      467
Complex number, modulus      467
Complex number, multiplication rule      471
Complex number, parallelogram law of addition      469
Complex number, plane      468
Complex number, polar form      470
Complex number, pure imaginary      465
Complex number, real part      465
Complex number, roots of unity      473 474
Complex subspacc      311
Component(s) of a vector      147
composition      365
Congruence      320
conic      25
Conjugate of a complex number      467
Conjugate transpose      304
Conjugate transpose of      304
Consistent and inconsistent      20
Consistent system ol'lincar equations      20
Constant term      1
Constant term, function      219
Constant term, matrix      5 50
Constant term, sequence      411
Constraints      482 486 489
containment      206
Contraction      351
Convergence of Fourier cense      463
Convergence of state vectors      101
Coordinate axes      147
Coordinate vectors      148
coordinates      147 372
Coordinates of a vector      372
Cosine of an angle      469
Cotactor      109
Cotactor, matrix      123
Cramer. G      127
Cramer’s Rule      127
Cross product      168
Dantzig, G      489
Davis, P J      439
Degree      191
Demand matnx      93
DeMoivre, A      472
DeMoivre’s Theorem      472
Dependent (linearly)      209
Descartes, Rene      187
Determinant      110
Determinant of block triangular matrix      118 391
Determinant of operator      386
Determinant, adjoini formula      125
Determinant, Cramer's rule      127
Determinant, formal definition      110
Determinant, Laplace expansion      110 111 136
Determinant, product theorem      120
Determinant, Vandcrmonde      134
Diagonal matrix      43 56
Diagonal matrix, operator      442
Diagonal matrix, orthogonally      283 445
Diagonal matrix, unitarily      308
Diagonalization      334—35
Diagonalization of a Hermitian matnx      110
Diagonalization of a matnx      262 310
Diagonalization of a quadratic form      114
Diagonalization of a system of differential equations      334—35
Diagonalization of an operator      441
Diagonalization, algorithm      262
Diagonalization, first order      244 331
Diagonalization, general solution      246 17 336
Diagonalization, initial condition      245
Diagonalization, linear system      332
Diagonalization, orthogonal      283 441
Diagonalization, second order      245 131
Difference      16 188 191
Differential equations      244 331
Differential equations, boundary condition      245 336
Differential equations, characteristic polynomial      245
Dilation      35
DIMENSION      14
Dimension of a subspace      223
Dimension, theorem      357
Direct sum      195
Direct sum of invariant subspaces      97
Direction cosines      165
Direction vector      150
Discnminant      475
Distance      156 425 448
Distributive property      48
Dot product      44 270
Dot product of geometric vectors      157
Doubly stochastic matrix      105
Economic models      90
Eigenspace of a matnx      252
Eigenspace of an operator      392
Eigenvalues      251
Eigenvalues of a matrix      251
Eigenvalues of an operator      392
Eigenvalues, complex      301 306
Eigenvalues, dominant      298
Eigenvalues, multiplicity of      265 394
Eigenvalues, positive      289
Eigenvalues, power method for finding      298
Eigenvalues, real      256 444
Eigenvectors      251 306 392
Eigenvectors of a matrix      251
Eigenvectors of an operator      392
Eigenvectors, basis of      262 441 445
Eigenvectors, dominant      298
Eigenvectors, independent      262 441
Electrical network      29
Elementary, column operation      78
Elementary, matrix      68
Elementary, operation      6
Elementary, row operation      8 68
ellipse      317
entries      33
Equality of functions      192
Equality of geometric vectors      141
Equality of linear transformations      346
Equality of matrices      35
Equality of n-tuples      187
Equality of polynomials      192
Equality of sequences      411
Equations differential      (see Differential equations)
Equations linear      (see Linear equations)
Equilibrium condition      92
Equilibrium in      92
Equilibrium in an economic system      92
Equilibrium in an economic system, condition for      92
Equivalent      6
Equivalent matrices      238
Equivalent matrices, Euclidean space      187
Equivalent matrices, inner product      421
Equivalent matrices, system of linear equations      6
Evaluation map      352 359
Evaluation of a polynomial      201 260
Evaluation of a polynomial at a matrix      260
Evaluation of a polynomial at the shift operator      417
Even polynomial      219
Even polynomial, function      462
Expansion theorem      273 433
Exponent law      471
Exponent law, bounded      486
Exponent law, bounding hyperplane      486
Exponent law, comer point      486
Exponent law, feasible region      482 486
Exponent law, lactor theorem      239
Extreme point      486
Extreme point, Binet, formula      416
Extreme point, Fibonacci sequence      416
Extreme point, generalized      419
Finite dimensional      214
Fixed line      452
Fixed line, axis      459
Fixed line, Hows in a network      27
Fixed line, hyperplane      458
Fixed line, plane      456
Fixed line, vector      459
Formula      156 468
Forward substitution      79
Fourier approximation      462
Fourier approximation, coefficients      433 461
Fourier approximation, series      463
Fourier, J B J      433
Function      192 339
Function, action of      192
Function, constant      219
Function, continuous      422
Function, differentiable      202
Function, distance preserving      460
Function, even/odd      462
Function, linear transformations      339
Function, objective      482 486 489
Function, pointwise operations      192
Fundamental identities      367
Fundamental theorem of algebra      477
Fundamental theorem of vector spaces      212
Gass. S      1 481 492
Gauss, K F      17 477
Gaussian algorithm      12 17
Gaussian algorithm, elimination      10 13
Generalized      402
Generalized inverse      325 31
Geometric vector      141
Gram — Schmidt algorithm      275 4 4
Gram, J P      275
Group of operators      460
Half plane      482
Hamilton, W R      407
Hcrstein, I N      408
Hcssenberg form      301
Hermite, C      305
Hermitian matrix      105
Homogeneous system of equations      24
Homogeneous system of equations, associated      50
Hooke's law      184 249
Householder matrices      301
Hyperbola      317
Hyperbola, idempotent matrix      56 68
Hyperbola, operator      401
Identity, linear transformation      343
Identity, matrix      45
Image of a linear transformation      351 352
Imaginary, axis      468
Imaginary, part of a complex number      465
Imaginary, unit      465
Inconsistent system      20
Independent (linearly)      209
Indeterminate      192
Index of a quadratic form      321
Induction, hypothesis      503
Induction, mathematical      501 502
Inequality, Bessel's      441
Inequality, Cauchy      428
Inequality, Cauchy — Schwarz      165
Inequality, Schwarz      427
Inequality, triangle      165 428 468
Initial point      141
1 2 3 4
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