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

Model, predator-prey      56
Model, relaxation      86
modus ponens      266
Multiplication, $\mu$ ultiplication      214
Multiplication, matrix      178
Multiplication, scalar      9 46
Multiplicative identity      180
Multiplicative inverse      185
Natural numbers      38 265
Natural transformation      259
Nested subspace      44
Nonsingular matrix      185
Norm on an inner product space      140
Normal vector      146
Normal vector to a plane      291
Normalization      157
Null space of a linear function      245
Nullity of a linear function      251
Odd function      162
Odd permutation      296
One-to-one function      219
Onto function      219
Ordered basis      124
Orientation      292
Orthogonal matrix      324
Orthogonal projection      146
Orthogonal set      155
Orthogonal vectors      145 152
Orthonormal set      158
Parallelogram law      142
Parallelogram path      340
Parallelogram rule      46
Parallelogram, area of      277 290
Permutation      296
Permutation, even      296
Permutation, odd      296
Peterson graph      340
Pivoting      84
Plane      51
Plane, direction vector for      51
Polarization identity      142
Polynomial      44
Polynomial, Chebyshev      172
Polynomial, Hermite      171
Polynomial, Laguerre      171
Polynomial, Legendre      171
Polynomial, orthogonal      170
Population model      192 207
Positive-definite property for a norm      150
Positive-definite property for an inner product      136
Power method      342
Predator-prey model      56
Prime number      122
Principle of complete mathematical induction      273
Principle of Mathematical Induction      267
Product, cross      288 289 290
Product, dot      137
Product, inner      136
Product, matrix      178
Projection onto a subspace      163
Projection onto a vector      152
proof      13
Proof by contradiction      115 253
Proof technique      6 13 14 107 115 267
Pythagorean Theorem      143 148 162
Quotient space      54
Raleigh quotient      342
RANGE      33 213
Rank of a linear function      251
Rank of a matrix      188
Rational numbers      114
Real numbers      5
Reduced row-echelon form      72
Reduction, Gauss — Jordan      69
Reflexive property      310
Reflexivity      53
Regression analysis      85
Regular Markov chain      196
Relaxation model      86
Right inverse      185

Right-hand rule      294
Right-handed basis      292
Rodrigues' formula      171
Rotation      227 232 238 293 295 306
Row of a matrix      29
Row operation and determinant      275
Row operation, elementary      70
Row operation, inverse      74 190 249
Row space      248
Row-echelon form      72
scalar      9
Scalar multiplication      9 46
Scalar multiplication, for matrices      30
Scalar multiplication, function      169 217 225
Sensitivity      298
Sequence, infinite      38
Series of matrices      201 203
Set      2
Shifted power method      343
Sierpinski's triangle      259
Sign of a permutation      296
Similar matrices      310
Similarity class      310
Snowflake curve      96
Solution of a differential equation      332
Solution of a linear system      62
Solution, set      62
Solution, trivial      77
span      97 129
Spectral theorem      326
Spectrum      326
Square matrix      179
Standard basis for $\mathbb R^3$       288 292
Standard basis for Euclidean space      112
Standard inner product      138
State of a Markov chain      194
Stein, Gertrude      45
Subset      3
subspace      39
Subspace Theorem      40
Subspace, nested      44
Substitution      15
Subtraction      18
Symmetric linear operator      324
Symmetric matrix      321
Symmetric property      310
Symmetry      53
System of differential equation      331
System of linear equations      62
Theorem      13
Topological vector space      170
Trace      310
Transition matrix      194
Transitive property      310
Transitivity      53
Translation function      169 225
Translation vector      50 51 184
TRANSPOSE      217 280
Transpose, determinant of      281
Transposition      296
Triangle inequality      150
Trivial solution      77
union      3
Uniqueness theorem      14
Unit vector      158
Vandermonde matrix      287
Variable, free      76 118
Variable, leading      76 118
Vector      9
Vector field      55
Vector field, linear      56
Vector space      9
Vector space with integer scalars      130
Vector space with rational scalars      114
Vertex of a graph      340
wronskian      334
Zero function      217 233 250
Zero matrix      183 276
Zero vector      10 16 17
Zorn's lemma      130

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