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Robinson D.J.S. — A Course in Linear Algebra with Applications
Robinson D.J.S. — A Course in Linear Algebra with Applications

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Название: A Course in Linear Algebra with Applications

Автор: Robinson D.J.S.

Аннотация:

The book is an introduction to Linear Algebra with an account of its principal applications. It is addressed to students of mathematics, the physical, engineering and social sciences, and commerce. The reader is assumed to have completed the calculus sequence. Special features of the book are thorough coverage of all core areas of linear algebra, with a detailed account of such important applications as least squares, systems of linear recurrences, Markov processes, and systems of differential equations. The book also gives an introduction to some more advanced topics such as diagonalization of Hermitian matrices and Jordan form. A principal aim of the book is to make the material accessible to the reader who is not a mathematician, without loss of mathematical rigor. This is reflected in a wealth of examples, the clarity of writing and the organization of material.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 422

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition of linear operators      205
Addition of matrices      7
Adjoint of a matrix      92
Algebra      208
Algebra of linear operators      205
Algebra of matrices      210
Angle between two vectors      216
Associative law      14 28 32 111
Augmented matrix      3
Back substitution      38 42
Basis of a vector space      133
Basis of a vector space, change of      188
Basis of a vector space, ordered      140
Bijective function      170
Bilinear form      365
Bilinear form, matrix representation of      366
Bilinear form, skew-symmetric      369 375
Bilinear form, symmetric      369
Block, Jordan      390
Cauchy — Schwartz inequality      216 237
Cayley — Hamilton theorem      386
Change of basis      188
Change of basis and linear transformation      192
Characteristic equation      291
Characteristic polynomial      290 294
Codomain      169
Coefficient matrix      3
Cofactor      75
Column echelon form      56
Column expansion      76
Column operation      55
Column space      147
Column vector      4
Commutative law      14 28 29 1
Companion matrix      307
Complex inner product space      241
Complex scalar product      229
Complex transpose      228
Composite of functions      171
Congruent matrices      368
Congruent matrices, eigenvalues of      373
conic      348
Consistent linear system      42
Coordinate vector      140
Cost matrix      17
Cramer's rule      97
Critical point      271 359
Crossover diagram      69
Determinant of a product      90
Determinant, definition of      73
Determinant, properties of      80
Diagonal matrix      5
Diagonalizable matrix      299
Differential equations      126
Differential equations, system of      322
DIMENSION      137
Dimension formulas      157 201 245
Direct sum of subspaces      160
Distance from plane      218
Distributive law      14 28 111
Domain of a function      169
Echelon form      42
Eigenspace      290
Eigenvalue      288 298
Eigenvalue of hermitian matrix      335
Eigenvector      287 297
Elementary column operation      55
Elementary matrix      53
Elementary row operation      47
Equations, linear      3 35
Equations, linear, homogeneous      44
Equivalent linear systems      40
Euclidean space      102 235
Even permutation      69
Expansion column      76
Expansion row      76
Factorization, QR-      260
Fibonacci sequence      314
Field axioms of a      29
Field of two elements      30
Filippov      381
Finitely generated      118
Function      169
Fundamental subspaces      147 248
Fundamental theorem of algebra      2
Gauss — Jordan elimination      43
Gaussian elimination      39
General solution      40
Gram — Schmidt process      256
Group general linear      32
Group of $\mathrm{n} \times \mathrm{n}$ matrices      32
Group, axioms for      32
Hermitian matrix      335
hessian      362
Homogeneous linear differential equation      127
Homogeneous linear system      44
Identity element      28 32
Identity function      170
Identity linear operator      180
Identity matrix      5
Image of a function      169
Image of a linear transformation      198
Inconsistent linear system      40
Indefinite quadratic form      354
Infinitely generated      119
Injective function      170
Inner product      232
Inner product space      234 241
Inner product, complex      241
Inner product, real      232
Inner product, standard      233
Intersection of subspaces      155
Intersection of subspaces, finding basis of      162
Inverse of a function      173
Inverse of a matrix      20 59
Inversion of natural order      69
Invertible function      173
Invertible matrix      20
Isomorphic algebras      210
Isomorphic vector spaces      204
Isomorphism      203 210
Jordan block      390
Jordan normal form      391
Jordan string      390
Kernel      198
Law of inertia      374
Laws of exponents      26
Laws of matrix algebra      14
Least squares solution      270
Least squares, method of      268
Least squares, method of, and QR-factorization      277
Least squares, method of, geometric interpretation of      279
Least squares, method of, in inner product spaces      282
Length of a vector      214
Line segment      103
linear combination      116
Linear dependence      121
Linear differential equation      127
Linear independence      122
Linear mapping      177
Linear operator      177
Linear recurrence      308
Linear system of differential equations      322
Linear system of equations      3 35
Linear system of recurrences      311
Linear transformation      177
Linear transformation matrix representation of      181
Linearly dependent      121
Linearly independent      122
Lower triangular      5
Markov process      317
Markov process, regular      319
Mathematical induction      401
Matrices, addition of      7
Matrices, congruent      368
Matrices, equality of      2
Matrices, multiplication of      9
Matrices, scalar multiplication of      7
Matrices, similar      196
Matrix, definition of      1
Matrix, diagonal      5
Matrix, diagonalizable      299
Matrix, elementary      53
Matrix, hermitian      335
Matrix, identity      5
Matrix, indefinite      354
Matrix, invertible      20
Matrix, negative definite      354
Matrix, non-singular      20
Matrix, normal      343
Matrix, orthogonal      262
Matrix, partitioned      23
Matrix, permutation      71
Matrix, positive definite      354
Matrix, powers of      12
Matrix, scalar      5
Matrix, skew-Hermitian      345
Matrix, skew-symmetric      14 376
Matrix, square      4
Matrix, symmetric      14
Matrix, triangular      5
Matrix, triangularizable      303
Matrix, unitary      265
Maximum, local      359
Method of least squares      268
Minimum polynomial      383
Minimum, local      359
Minor      74
Monk polynomial      383
Multiplication of matrices      9
Negative definite matrix      354
Negative definite quadratic form      354
Negative of a matrix      7
Negative of a vector      111
Negative semidefinite      364
Non-singular      20
Norm      236 238
Normal form of a matrix      57 151
Normal matrix      343
Normal system      272
Normed linear space      238
Null space of a matrix      115
Odd permutation      69
One-one      170
One-one correspondence      170
Onto      170
Operation, column      55
Operation, row      47
Optimal least squares solution      280
Ordered basis      140
Orthogonal basis      253
Orthogonal complement      242
Orthogonal linear operator      267
Orthogonal matrix      262
Orthogonal set      251
Orthogonal vectors      216
Orthogonality in $\mathbb{R}^\mathrm{n}$      225
Orthogonality in inner product spaces      234
Orthonormal basis      253
Orthonormal set      251
Parallelogram rule      105
Partitioned matrix      23
Permutation      67
Permutation, matrix      71
Pivot      42
Polynomial characteristic      290 294
Polynomial minimum      383
Positive definite matrix      354
Positive definite quadratic form      354
Positive semidefinite      364
Powers of a matrix      12
Powers of a matrix, negative      27
Principal axes      350
Principal diagonal      5
Product of determinants      90
Product of linear operators      206
Product of matrices      9
Projection of a vector on a line      217
Projection of a vector on a subspace      247
QR-factorization      260
Quadratic form      346
Quadratic form, indefinite      354
Quadratic form, negative definite      354
Quadratic form, positive definite      354
Quadric surface      351
Rank of a matrix      151
Real inner product space      232
Recurrence, linear      308
Recurrence, linear, system of      311
Reduced column echelon form      56
Reduced echelon form      43
Reduced row echelon form      51
Reflection      197
Regular Markov process      319
Right-handed system      223
Ring with identity      28
Ring with identity matrix over      30
Ring with identity of $\mathrm{n} \times \mathrm{n}$ matrices      31
Rotation      178 184 191 264
Row echelon form      48
Row expansion      76
Row operation      47
Row space      147
Row vector      4
Row-times-column rule      9
Saddle point      359
Scalar matrix      5
Scalar multiple of a linear operator      205
Scalar multiple of a matrix      7
Scalar multiplication      7
Scalar product      213
Scalar projection      217
Schur's theorem      337
Sign of a permutation      71
Similar matrices      196
Singular matrix      20
Skew-Hermitian matrix      345
Skew-symmetric bilinear form      369 375
Skew-symmetric matrix      14 376
Solution space      115 324
Solution, general      40
Solution, non-trivial      44
Solution, trivial      44
Spectral theorem      339
Standard basis of $\mathbb{R}^\mathrm{n}$      134
Standard basis of $\mathrm{P}_\mathrm{n}\left(\mathbb{R}\right)$      138
String, Jordan      390
subspace      113
Subspace, fundamental      147 248
Subspace, generated by a subset      117
Subspace, improper      113
Subspace, spanned by a subset      117
Subspace, zero      113
Sum of subspaces      155
Sum of subspaces, finding a basis for      162
Surjective function      170
Sylvester's law of inertia      374
Symmetric bilinear form      369
Symmetric matrix      14
System of differential equations      322
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