Messer R. — Linear Algebra: Gateway to Mathematics :: Электронная библиотека попечительского совета мехмата МГУ

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Messer R. — Linear Algebra: Gateway to Mathematics

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Название: Linear Algebra: Gateway to Mathematics

Автор: Messer R.

Аннотация:

Since many students feel uncomfortable at first or unfamiliar with the theoretical nature of many topics in linear algebra, numerous discussions of the logical structure of proofs, the need to translate terminology into notations, and suggestions about efficient ways to discover a proof are discussed. "Crossroads" boxes showing students how topics fit together, quick examples, exercises with selected answers, references, chapter summaries, and chapter review exercises are included. Printed on acidic paper.

Язык:

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 560

Добавлена в каталог: 19.03.2005

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Предметный указатель

      112
vectors      288
$\mathbb C(X)$       43 44
$\mathbb D(X)$       44
$\mathbb D^\infty$       304
$\mathbb D^{(n)}(X)$       44
$\mathbb F(X)$       33
$\mathbb M(m, n)$       29
$\mathbb N$       2 265
$\mathbb P$       44
$\mathbb P_n$       44
$\mathbb Q$       114
$\mathbb Q$ -vector space      114
$\mathbb R$       5
$\mu_A$       214 228
$\varnothing$       5
Abel's formula      335
Absorbing Markov chain      199
Absorbing state of a Markov chain      199
Abstraction      10
Addition of matrices      30
Addition of vectors      9 46
Additive identity      10
Additive identity, property of      16
Additive identity, uniqueness      16
Additive inverse      10 18
Additive inverse, property of      17
Additive inverse, uniqueness      14
Additive property      213
Adjacency matrix      340
Adjacent vertex      340
Adjoint      283
Affine function      259
Affine space      54
Algebraic coding theory      130
Ambiguity      12 17 20 292
angle      143 151
Anticommutative law      289
Approximation theorem      164
Approximation, Fourier      166
Area of a parallelogram      277 290
Associative law of matrix multiplication      180
Associative law of scalar multiplication      10
Associative law of vector addition      9
Augmented matrix      64
Axiom, inner product      136
Axiom, norm      142
Axiom, vector space      9
Basis for a vector space      111
Basis for a vector space, left-handed      292
Basis for a vector space, ordered      124
Basis for a vector space, right-handed      292
Basis for a vector space, standard for $\mathbb R^3$       288 292
Basis for a vector space, standard for Euclidean space      112
Basis for induction      267 273
Baskin — Robbins      26
Bessel's equality      162
Bessel's inequality      168
Biconditional statement      105
Binomial theorem      205
Cancellation theorem      19
Cartesian product      25
Cauchy — Schwarz inequality      149
Cayley — Hamilton theorem      183 313
Change-of-basis matrix      240
Characteristic equation      305
Characteristic polynomial of a linear operator      312
Characteristic polynomial of a matrix      305
Chebyshev polynomials      172
Classification Theorem for finite-dimensional vector spaces      257
Closure      10 28 30
Closure, under addition      12 40
Closure, under matrix multiplication      179
Closure, under multiplication      11 12
Closure, under scalar multiplication      40
Codes, error-correcting      130
Codes, linear      130
Coefficient matrix      64
Cofactor      283
Column of a matrix      29
Column space      247
Commutative law      6
Commutative law and matrix multiplication      181
Commutative law for an inner product      136
Commutative law of vector addition      9
Comparison theorem      115
Complete graph      340
Complex conjugate      329
Complex number      325 329
Composition of functions      220
Composition of functions, matrix of      233
Conclusion      4 13
Connected graph      340
Continuity      169
Continuous function      43 44
Continuous matrix function      330
Contraction Theorem      117
CONVERSE      104
Coordinate vector      124
Coordinate vector, function      214 238
Cramer's rule      284
Cross product      288
Cross product, algebraic properties      289
Cross product, geometric properties      290
Curve fitting      81 297
Degree of a vertex      340
Derivative of a matrix function      206 333
Determinant      273
Determinant of a power      282
Determinant of a product      280
Determinant of a transpose      281
Determinant of an inverse      282
Diagonal matrix      312
Diagonalizable matrix      312
Differentiable function      44
Differentiable matrix function      330
Differential equation, linear      331
Differential equation, second-order homogeneous      338
Differential equation, system      331
DIMENSION      91 96 112
Dimension Theorem      251
Dimension, fractional      96
Direct sum      169
Direction field      55
Direction vector for a line      51
Direction vector for a plane      51 291
Distance      143
Distributive law for an inner product      136
Distributive law for matrices      180
Distributive law for vectors      10
Domain      33 213
Dot product      137
Dual space      258
Economic model      206
Edge of a graph      340
Eigenspace of a linear function      304
Eigenspace of a matrix      306
Eigenvalue of a graph      341
Eigenvalue of a linear function      304
Eigenvalue of a matrix      306
Eigenvalue, dominant      342
Eigenvalue, numeric method      341
Eigenvector of a linear function      304
Eigenvector of a matrix      306
Eigenvector, numeric method      341
Element      2
Elementary matrix      209
Elementary row operation      70
Elimination, Gaussian      69
Empty set      5

Empty set, linear combination      92 103 114
Empty set, linear independence      105 111 114
Entry of a matrix      29
Equivalence relation      53
Equivalence, logical      105 107
Error-correcting codes      130
Euclidean space      21 25
Euler characteristic      340
Euler's formula      339
Even function      162
Even permutation      296
Excluded middle, law of      115
Expansion Lemma      119
Expansion theorem      119
Fibonacci sequence      272
Field      130
Finite-dimensional vector space      112
Fourier approximation      166
Fourier series      166
Fractal      96 259
Free variable      76 118
Function      33 213
Function space      32
Function, continuous      44
Function, differentiable      44
Function, even      162
Function, identity      220
Function, linear      213
Function, odd      162
Function, one-to-one      219
Function, onto      219
functor      258
Fundamental matrix      201
Fundamental Theorem of absorbing Markov chains      201
Fundamental theorem of algebra      306 325
Fundamental Theorem of homogeneous systems      78
Fundamental Theorem of regular Markov chains      196
Gauss — Jordan reduction      69
Gaussian elimination      69
Golden mean      273
Gram — Schmidt orthonormalization process      159
Graph      340
Graph, complete      340
Graph, connected      340
Graph, Peterson      340
Hermite polynomials      171
Hessian matrix      322
Homogeneous property for a linear function      213 218
Homogeneous property for a norm      150
Homogeneous property for an inner product      136
Homogeneous system      77
Hypothesis      4 13
Identity function      169 217 220 233 239 250
Identity matrix      180 276
Identity, additive      10 16 17
If and only if      104 107
Image of a function      33 219 245
Implication      4 19 104
Indirect proof      115 253
Induction hypothesis      268
Inductive set of real numbers      270
Infinite-dimensional vector space      112 129
Initial condition      333
Initial distribution vector      194
Initial-value problem      333
Inner product      136
Inner product on a function space      138 142
Inner product on Euclidean space      138 142
Inner product space      136
Intersection      3
Intersection of subspaces      45
Inverse function      221
Inverse function, matrix of      2355
Inverse matrix      185
Inverse matrix, uniqueness of      185
Inverse power method      343
Inverse row operation      74 190 249
Inverse, additive      10 14 16 18
Inverse, multiplicative      185
inversion      296
Invertible matrix      185
Isomorphic vector spaces      256
Isomorphism      55 256
Iterated function system      259
Join      340
Kernel of a linear function      245
Laguerre polynomials      171
Laplace transform      217
Law of Cosines      154
Law of excluded middle      115
Leading      1 70
Leading entry      70
Leading variable      76 118
Left inverse      185
Left-handed basis      292
Legendre polynomials      171
Length      143
Line      51
Line, direction vector for      51
Linear codes      130
linear combination      92 129
Linear combination function      214 235 238
Linear dependence      104
Linear differential equation      331
Linear equation      62
Linear function      213
Linear function, coordinate vector      214 238
Linear function, identity      217 233 250
Linear function, inverse of      222
Linear function, linear combination      214 235 238
Linear function, matrix multiplication      214
Linear function, matrix of      230
Linear function, rotation      227 238
Linear function, scalar multiplication      217 225
Linear function, symmetric      324
Linear function, zero      217 233 250
Linear independence      104 129
Linear independence of eigenvectors      316
Linear independence of orthogonal vectors      157
Linear map      213
Linear model      206
Linear operator      213
Linear operator, symmetric      324
Linear programming      81 85
Linear transformation      213
Linearly dependent      104
Linearly independent      104
Logical implication      104
LU-Decomposition      84
Main diagonal      310
Markov chain      194
Markov chain, absorbing      199
Markov chain, absorbing state      199
Markov chain, initial distribution vector      194
Markov chain, regular      196
Markov chain, state      194
Markov chain, transition matrix      194
Mathematical induction, principle of      267
Mathematical induction, principle of complete      273
Matrix      29
Matrix function      330
Matrix function, continuous      330
Matrix function, differentiate      330
Matrix multiplication      178
Matrix, elementary      209
Matrix, of a linear function      230
Matrix, planet      276
Model, economic      206
Model, linear      206
Model, population      192 207

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