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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
Matrix, upper triangular      78
Matrix, values      251
Matrix, Vandermonde      116 134
Matrix, vectors      251
Matrix, zero matrix      36
Median of a tetrahedron, I      55
Median of a triangle      155
midpoint      150
Minor of a matrix      109
Mirkil, H      102
Mlpoient matrix      260
Modulus of a complex number      467
Moore — Penrose inv erse      331
Multiplication of matrices      43
Multiplication of matrices, properties of      47
Multiplication rule lor complex numbers      471
Multiplicity of eigenvalues      265 394
Multiplicity ol a root      265 394
n-tuple      187
Negative of a function      191
Negative of a geometric vector      142
Negative of a matnx      36 190
Negative of an H-inplc      188
Negative uniqueness of      194 197
Network flow      27
Network, electrical      29
Norm      303 425
Normal equations      180 325
Normal matrix      310
Normal vector for a plane      166
Normalizing      272 432
Null space of a linear transformation      353
Null space of a matrix      200
Null space of function      462
Null space of objective function      482 486 489
Null space of odd polynomial      219
Nullity oflincar transformation      354
One-to-one linear transformation      355
Onto linear transformations      355
Open scctor of an economy      93
Operator      (see Linear operator)
Ordered basis      371
Ordered n-tuple      187
Ordered n-tuple, dot-product      44 270
Ordered n-tuple, sum and difference      188
Ordered pair      187
Ordered triple      187
Origin      147
Orthogonal      277 436
Orthogonal, basis      273 433
Orthogonal, complement of a subspacc      277 436
Orthogonal, diagonalization      283 441
Orthogonal, lemma      274 434
Orthogonal, Matrix      281 450
Orthogonal, projection      278 437
Orthogonal, set of vectors      271 307 431
Orthogonal, vectors      157 160 307
Orthogonalizmion algorithm      275
Orthonormal set of vectors      271 307 431
Parallel vectors      142
Parallelepiped      174
Parallelogram, area of      173
Parallelogram, rule      143 469
PARAMETER      3 151
Parametric, equations ol a line      151
Parametric, lorm of solutions      2
Parseval’s formula      441
Partition, of a matrix      52
Permutation matrix      85 288 387
Pivot      492
Plane, complex      468
Plane, normal to      166
Plane, scalar equation      166
Plane, vector equation      167
PLU-factorization      86
Polar norm of a complex number      470
Polynomial      191
Polynomial, associated to a linear recurrence      414
Polynomial, characteristic      253 306
Polynomial, coefficients      191
Polynomial, degree      191
Polynomial, equality      192
Polynomial, evaluation at a matrix      260
Polynomial, evaluation at the shill operator      417
Polynomial, evaluation of      201 260
Polynomial, even      219
Polynomial, factor theorem      239
Polynomial, fundamental theorem of algebra      477
Polynomial, interpolating, I      32
Polynomial, Lagrange interpolation expansion for      242
Polynomial, Lagrange polynomials      242
Polynomial, Legendre polynomials      436
Polynomial, odd      219
Polynomial, remainder theorem      239
Polynomial, root      201
Polynomial, Taylor's theorem lor      24
Polynomial, vector space ot      192
Polynomial, zero polynomial      191 192
Position vector of a point      147
Positive definite, matrix      289 293 424
Positive definite, quadratic form      321
Positive vector ol a point      147
Power method      298
Pre-image of a subspace      351
principal argument      470
Principal argument, submatrix      291
Principal Axes Theorem      283 445
Principle of Mathematical Induction      502
Probabilities      96
Product of matrices      44
Product theorem for determinants      120
Projection      162 278 4
Projection, linear operator      448
Projection, matrix      281 288
Projection, orthogonal      277 437
Projection, theorem      278 437
Pythagorean Theorem      156 165 272 432
Quadratic equation      323
Quadratic form      313 425
Quadratic form, completely dtagonali/ed      321
Quadratic form, diagonalization of      3 3
Quadratic form, index of      321
Quadratic form, positive definite      323
Quadratic form, principal axes for      115
Quadratic form, rank of      321
Quadratic form, Sylvester's law      320
Quadratic, discriminant of      475
Quadratic, formula      475
Quadratic, irreducible      475
Quadratic, real      475
Radian measure      469
Range of a linear transformation      353
Range of a matrix      200
Rank of a linear transformation      354
Rank of a matrix      21 230
Rank of a quadratic form      321
Rayleigh quotients      298
Real axis      468
Real eigenvalues      256 444
Real part of complex numbers      465
Recurrence relation, associated polynomial      414
Recurrence relation, length      412
Recurrence relation, linear      267 411
Recurrence relation, space of solutions      411
Reduced      11
Reducible linear operator      397
Reflection      343 349 452 458
Relation to invertibility      231
Relation to null space      21 234
Relation to null space, theorem      229
Remainder theorem      239
Restriction of a linear operator      389
Rhombus      161
Right-hand coordinates      175
Right-hand rule      175
Root of a polynomial      201
Root of a quadratic      475
Root of unity      473 474
Root, complcx      475
Root, multiplicity of      265 394
Rotations      343 349 458
Row matnx      34
Row of a matrix      34
Row operations      8 68
Row operations for determinants      113
Row space      228
Row-cchelon matnx      11
Row-echelon form      11
Row-equivalent matrices      77
scalar      38 189
Scalar equation of a plane      166
Scalar linear transformations      343
Scalar matnx      105
Scalar multiplication      38 144 189
Scalar multiplication of functions      192
Scalar multiplication of geometne vectors      144
Scalar multiplication of linear transformations      406
Scalar multiplication of matrices      38
Scalar multiplication of n-tuples      188
Scalar multiplication of polynomials      192
Scalar product      157
Schmidt. E      275
schur      1 308
Schur’s Theorem      309
Schwarz inequality      427
Schwarz, H A      427
Seneta, B      92
Sequences      411
Sequences, constant      411
Sequences, equality      411
Sequences, Lucas      419
Sequences, power      411
Sequences, satisfying a linear recurrence      411
Sequences, vector spaccof      411
Shear      342
Shift operator      417
Signature of a quadratic form      383
Similar, matrices      256 383
Similar, orthogonally      362
Similarity invariant      257 383
simple harmonic motion      248
Simplex algorithm      4
Simplex algorithm, basic columns      491 495
Simplex algorithm, basic feasible solutions      491 495
Simplex algorithm, basic variables      491 495
Simplex algorithm, degeneration      499
Simplex algorithm, departing variable      493
Simplex algorithm, entenng variable      492
Simplex algorithm, flow chart      496
Simplex algorithm, objective function      482 486 489
Simplex algorithm, pivot columtt      492
Simplex algorithm, pivot entry      492
Simplex algorithm, prototype example      490
Simplex algorithm, unbounded      494
Sine of an angle      469
Size of a matnx      34 38
Skew — Hermitian matrix      312
Skew-symmetnc matrix      43
Skew-symmetnc matrix, operator      448
Slack variables      490
Slack variables, tableau      495
Snell, J. L      102 481
Solutions to a system of equations      2
Solutions to a system of equations, general      3
Solutions to a system of equations, linear combinations      55
Span of a set of vectors      204
Spanning set      204
Spanning set for      204
Spectral theorem      310
Spectral theorem, real      284
Spectrum      284
Spring constant      249
Square matrix      34
Standard, basis      214 303
Standard, inner product in C      303
Standard, matrix of a linear transformation      349
Standard, position for an angle      469
Stewart, G. W      301
Stochastic matrix      91 99
Stochastic matrix, basis of      223
Stochastic matrix, complement of      395
Stochastic matrix, complex      311
Stochastic matrix, dimension of      223
Stochastic matrix, direct sum of      395
Stochastic matrix, doubly      105
Stochastic matrix, intersection of      219 394
Stochastic matrix, invariant      388
Stochastic matrix, orthogonal complement of      277 436
Stochastic matrix, pre-image of      351
Stochastic matrix, projection on      278
Stochastic matrix, regular      102
Stochastic matrix, subspace      198
Sum of      226 394
Sum of functions      192
Sum of geometric vectors      143
Sum of linear transformations      379
Sum of matrices      35
Sum of ordered n-tuples      188
Sum of solutions to equations      50
Sum of subspaces      226 394
Sum of test      198
Sum of zero subspace      199
Sum, pointwise      192
Sylvester’s law of inertia      320
Symmetric, bilinear form      324
Symmetric, matrix      42 283
Symmetric, operator      444
System of linear equations      1
Taylor’s Theorem      240
Terminal point      141
tetrahedron      155
Thompson, G. L      102 481
Tnangulation algorithm      404
Transformations, tee linear transformations trace of a matrix      56 257
Transformations, tee linear transformations trace of an operator      386
Transition matrix for Markov chain      98
Transition probabilities      96 98
Translation      460
TRANSPOSE      41
Triangle, altitude of      161
Triangle, centroid of      155
Triangle, inequality      165 428 468
Triangle, median of      155
Triangular matrix      90
Triangular matrix, angle between      156
Triangular matrix, block      118
Triangular matrix, components      147
Triangular matrix, cross product      168
Triangular matrix, direction vector ol a line      150
Triangular matrix, distance formula      156
Triangular matrix, dot product      157
Triangular matrix, equality      141
Triangular matrix, equation of a line      151
Triangular matrix, equation of a plane      167
Triangular matrix, initial point      141
Triangular matrix, Jacobi identity      177
Triangular matrix, Lagrange identity      172
Triangular matrix, length      141
Triangular matrix, lower      78
Triangular matrix, magnitude      141
1 2 3 4
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