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Usmani R.A. — Applied Linear Algebra
Usmani R.A. — Applied Linear Algebra

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Название: Applied Linear Algebra

Автор: Usmani R.A.

Аннотация:

This text is designed for a course in linear algebra and some of its applications for beginning students of science and engineering. It is an outgrowth of the notes from which I have lectured in recent years to undergraduate students of science and graduate students of the Faculty of Engineering at the University of Manitoba. I have found that an average student of science or engineering finds the vast existing literature on the theory and applications of matrices rather formidable, and I hope that the present text will develop understanding and grasp of the basic concepts. It will also bridge the gap between elementary books and the more advanced volumes on the subject.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 259

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute convergence      181
Adjoint of a matrix      42 171
Analytic      183
Applications of positive definite matrices      165
Augmented matrix      40f 216
Band matrices      45
Basis of a vector space      16
Binary operation      1f
Cauchy — Schwarz inequality      24
Cayley — Hamilton theorem      156 170
Change of basis      118
Characteristic equation      123
Characteristic value      see "Eigenvalue"
Characteristic vector      see "Eigenvector"
Chebib, F.      78
Choleski's decomposition      207
Cofactor      41
Column rank      56
Conjugate transpose      84
Consistent system      82f 91 216
Cramer's rule      216 220
Determinant      212
Difference equation      46 156 206
Differential equation      132 185
Differentiation of a matrix      183
Dimension of a vector space      16
Discretization error      207
Eigenvalue      123
Eigenvalues of a band matrix      135
Eigenvalues of a circulant matrix      140
Eigenvalues of a companion matrix      138
Eigenvector      123
Elementary column operations      40
Elementary matrices      62
Elementary row operations      40
Error equation      207
Exp (A)      182 187
Factor analysis      167
Fibonacci sequence      160
Field      1
Finite difference method      206
Finite field      3
Fischer, C.F.      48
Full column rank      83
Full rank factorization      93
Full row rank      88
Functions of a matrix      170f
Gauss — Jordan reduction      40f 217
Generalized eigenvectors      150f
Generalized inverse      65f
Gershgorin theorem      162
Goldberg, S.      158
Graph of a matrix      197
Graph of a matrix, strongly connected      197
Greville, T.N.E.      71
Henrici, P.      203 209
Hermitian matrix      88 128
Homogeneous linear equations      60f
Inconsistent system      82 216
Index of $\lambda_{i}$      176
Inner product      23 143
Integration of a matrix      183
Inversion of a matrix      37
Isomorphism      104
Jordan's block      149 176
Jordan's box      149
Jordan's canonical form      149f 175f
Kantorovich, L.V.      211
Konig, D.      198
Kuttler, J.R.      204
l'Hopital's rule      5f
Laplace methods of expanding determinant      46 124f
Laplace transform method      187
Lawson, C.L.      79 167
Least squares solution      81f
Left inverse      65f
Linear dependence      16 126
Linear difference equations      see "Difference equation"
Linear differential equations      see "Differential equation"
Linear equations      12f 39 214
Linear transformation      101f
Linear transformation, null of      103
Linear transformation, perpendicular projection of      103
Linear transformation, range of      103
Linear vector space      see "Vector space"
Marsden, M.J.      209
Matrix      9
Matrix of a linear transformation      108
Matrix, adjoint      42
Matrix, band      45
Matrix, circulant      140
Matrix, companion      113 138
Matrix, defective      132
Matrix, diagonal      9 43
Matrix, diagonally dominant      200
Matrix, elementary      62
Matrix, five-band      51 202
Matrix, hermitian      58 128
Matrix, identity      9
Matrix, irreducible      194
Matrix, lower triangular      43
Matrix, monotone      194 202
Matrix, negative definite      160
Matrix, nilpotent      181
Matrix, nonnegative      198
Matrix, nonsingular      38
Matrix, null      10
Matrix, orthogonal      145 147
Matrix, permutation      1
Matrix, positive definite      160
Matrix, reducible      194
Matrix, scalar      9
Matrix, singular      38
Matrix, skewsymmetric      34
Matrix, square      9
Matrix, symmetric      34
Matrix, unit      9
Matrix, upper triangular      43
Matrix, zero      10
Meek, D.S.      230
Minimum polynomial      172f
Monic polynomial      172f
Moore — Penrose inverse      84
Newton's method      210
Noble, B.      42
Norm      22
Norm of a matrix      22
Norm of a vector      22
Null space of a matrix      60
One-2-3 inverse      84
One-2-4 inverse      84
One-inverse      84f
Orthogonal matrix      147f
Orthogonal set of vectors      143
Partitioning      31 194
Perron — Frobenius theorem      199
Plate deflection theory      209
Polynomial, characteristic      124f
Polynomial, minimum      172
Polynomial, monic      172
Positive definite matrix      160
Power series      179
Principle of least squares      72f
Principle of Mathematical Induction      39 115 138 144 147 150 157
Product of two linear transformations      115
Proper value      see "Eigenvalue"
Proper vector      see "Eigenvector"
Pseudo-inverse      84
Range of a matrix      63
Rank of a matrix      56
Rational function      3
Reduced column echelon form      55
Reduced row echelon form      55 217
Reflection      106
Relative maxima      74
Relative minima      74
Right inverse      65f
Rotation of plane      102
Rounding errors      208
Row equivalent matrix      54
Row rank of a matrix      56
Rutherford, D.E.      49 228
Scatter diagram      73
Sequence of matrices      179
Set      1
Shoosmith, J.N.      205
Similar matrices      120
Skew-Hermitian      88
Spanning set      15
Spectral radius      180
Spectral theorem      143f
subspace      13
Subspace, column space      54f
Subspace, null space      60
Subspace, row space      54f
Substitution, back      207
Substitution, forward      207
Sylvester theorem      177
Trace      35
Transition matrix      115f
Transposition      34
Two-point boundary value problem      205
Two-point boundary value problem, linear      205f
Two-point boundary value problem, nonlinear      209f
Usmani, R.A.      48 53 78 209 230
Vandermonde matrix      118
Varga, R.S.      198 199
Vector space      4
Vector space, basis of a      16f 18
Vector space, dimension of a      16f 18
Vector, column      9
Vector, row      9
Weak row sum criterion      203
Wronskian determinant      21
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