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Lipschutz Seymour Ч Schaum's Outline of Theory and Problems of Linear Algebra (Schaum's Outlines)
Lipschutz Seymour Ч Schaum's Outline of Theory and Problems of Linear Algebra (Schaum's Outlines)

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Ќазвание: Schaum's Outline of Theory and Problems of Linear Algebra (Schaum's Outlines)

јвтор: Lipschutz Seymour

јннотаци€:

An updated, revised edition of this very successful Schaum's Outline. Chapters 1 and 3 have been combined so the text begins with linear equations. Chapters 4 (Vector Space Analysis) and 5 (Basis and Dimension) are combined and there is an additional chapter on the cross product and applications of the delta function. There are hundreds of solved and supplementary problems.


язык: en

–убрика: ћатематика/јлгебра/Ћинейна€ алгебра/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1991

 оличество страниц: 368

ƒобавлена в каталог: 14.05.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$C^n$      52Ч53 72
$K^n$      142
$R^n$      40Ч41 53Ч54
Absolute value      52
Adjoint operator      425Ч426 433Ч436
Adjoint operator, matrix representation      426
Adjoint, classical      253Ч254
Algebra of linear maps      322
Algebraic multiplicity      285
Algorithm, basis-finding      154
Algorithm, determinant      253
Algorithm, diagonalization under, congruence      102Ч104
Algorithm, diagonalization under, similarity      102 286
Algorithm, Elimination (Gaussian)      8 24Ч25 100 261
Algorithm, Euclidean      446
Algorithm, Gauss Ч Jordan      29
Algorithm, inverse matrix      100
Algorithm, orthogonal diagonalization      289
Alternating bilinear form      411
angle      45 206
Annihilators      399Ч400 403Ч404
Arbitrary permutations      249
Augmented matrix      78
A{V)      322
B(V)      409
Back-substitution      9
Basis, dual      398 400Ч403
Basis, general solution      19Ч20
Basis, orthogonal      208
Basis, second dual      399
Basis, usual      150
Basis, vector space      150 169Ч171
Basis-finding algorithm      154
Bessel inequality      212
Bijective mapping      314
Bilinear form      409 414Ч416
Bilinear form, alternating      411
Bilinear form, Bilinear form, polar form of      412
Bilinear form, matrix representation of      410
Bilinear form, rank of      411
Bilinear form, real symmetric      412Ч413
Bilinear form, symmetric      411Ч412
Block matrix      79Ч80 86
Block matrix, determinant of      256Ч257
Block matrix, diagonal      98 291
Block matrix, Jordan      374
Block matrix, square      98 123Ч124
Block matrix, triangular      98
Cancellation law      142
Canonical form      14 352
Canonical form, Jordan      373Ч374 381Ч385
Canonical form, rational      375Ч376 388Ч390
Canonical form, row      14 16 28Ч30
Cauchy Ч Schwarz inequality      45 58 205Ч206 218
Cayley Hamilton theorem      282 302Ч304 307
cells      79
Change of basis      159Ч162 187Ч191
Change-of-basis matrix      160 348 357Ч359
Change-of-variable matrix      105Ч106
Characteristic polynomial      281Ч284 349
Classical adjoint      253Ч254
Codomain      312
Coefficient      1
Coefficient matrix      17 78
Coefficient, Fourier      211
Cofactor      252
column      13 74
Column, operations      100Ч102
Column, rank      152
Column, space      146
Column, vector      40 75
Commuting matrices      90
Companion matrix      291 375
Complement, orthogonal      207Ч208 226
Complex, conjugate      51
Complex, inner product      216Ч218
Complex, matrix      96 121Ч122
Complex, n-space      52
Complex, numbers      51
Component      40 211
Composition of mappings      313
Congruent, diagonalization      102Ч103
Congruent, matrices      102 410
Congruent, symmetric matrices      102Ч103 124Ч125
Conjugate matrix      96
Conjugate, complex      51
Consistent systems      13
Convex set      342 407
Coordinate vector      157 186Ч187
coordinates      40 157Ч159
cosets      376
Cramer's rule      255 263Ч264 268
Cross product      49Ч50 65Ч67
CURVES      48
Cyclic subspaces      374Ч375 388Ч389
Degenerate linear equations      2 3
Degree of polynomial      446
Dependence, linear      147 166Ч169
Determinant      246
Determinant, block matrix      256Ч257
Determinant, computation of      253 260Ч262
Determinant, linear equations      254Ч255
Determinant, linear operators      349
Determinant, multiplinearity      257Ч258
Determinant, order      3 248
Determinant, order n      250
Determinant, properties      251Ч252
Determinant, volume      257
Diagonal (of a matrix)      90
Diagonal matrix      93Ч94
Diagonal matrix, block      98
Diagonalizable matrices      280 288Ч289 298Ч301
Diagonalization      349Ч350 360Ч363
Diagonalization algorithm      102Ч104 286Ч288
Dimension of solution spaces      19
Dimension of vector spaces      150Ч151
Dimension of vector spaces, subspaces      151 171Ч172
Direct sum      156 181Ч186
Direct sum, decomposition      371 379Ч380
Directed line segment      46
Distance      45
Domain      312
Dot product      43Ч46 52 56Ч57
Dual basis      398
Dual space      397
Echelon form      10Ч11 14 23Ч24
Echelon matrices      14
Eigenvalue      284Ч285 292Ч298 350
Eigenvalue, computing      286Ч287
Eigenvector      284Ч286 292Ч298 350
Eigenvector, computing      286Ч287
Elementary divisors      376
Elementary matrix      99 101 117Ч118
Elementary operations      7Ч8
Elementary operations, column      100Ч102
Elementary operations, row      14 98Ч100
Elimination algorithm      6
Elimination, Gaussian      8 24Ч26 100 261
Enenspace      284 350
Equal matrices      74
Equal vectors      40
Equations      See Linear equations
Equivalence, matric      100 102
Equivalence, row      14 16
Equivalent systems      7Ч8
Euclidean algorithm      446
Euclidean space      203
Evaluation map      92
Factorization, LU      109Ч111 130Ч133
Factorization, polynomial      448
Field      74
Finite dimension      150Ч151
Fourier coefficient      211
Free variable      3 10
Function, spaces      143
Function, square matrix      89Ч90
Functional, linear      397
F{X)      143
Gauss Ч Jordan algorithm      29
Gaussian elimination      8 24Ч26 100 261
General solution      1 7
Geometric multiplicity      285
Gram Ч Schmidt orthogonalization      213
Graph      4
Greatest common divisor      447
Hermitian form      413Ч414
Hermitian matrix      97
Hermitian quadratic form      414
Hilbert space      205
Homogeneous systems      18Ч20 32Ч34 399Ч400
Hyperplane      46 407
Identity mapping      314
Identity matrix      91
ijk notation      49
Im F      316
Im z      51
Image of linear mapping      316Ч318 328Ч331
Imaginary part      51
Inconsistent systems      13
Independence, linear      147Ч150
Infinite dimension      150
Infinity-norm      219
Injective mapping      314
Inner product      202 221Ч226
Inner product spaces      202Ч205
Inner product spaces, linear operators on      425
Inner product, complex      216Ч218
Inner product, usual      203 214Ч216 218
Invariance      370Ч371
Invariant subspaces      370Ч371 377Ч378
Inverse matrix      92
Inverse matrix, computing algorithm      100
Invertible matrices      92Ч93 115Ч117
Invertible matrices, linear substitutions      105
Invertible matrices, operators      323
Isomorphic vector spaces      316
Isomorphism      158Ч159 316 320
Jordan block      374
Jordan canonical form      373Ч374
Ker F      316
Kernel of a linear map      316Ч320 328Ч332
Kronecker delta      91
Laplace expansion      252
Law of inertia      102 413
Leading nonzero entry      13
Leading unknown      3
Length      44 203
Line      47
linear combination      19 41Ч42 145Ч147 149 165Ч166
Linear dependence      42Ч43 147Ч149 166Ч169
Linear equation      1
Linear equation, degenerate      2Ч3
Linear equation, one unknown      2
Linear equations (system)      1 21 152Ч153 319Ч320 323Ч324 399Ч400
Linear equations (system), consistent      13
Linear equations (system), echelon form      10 23Ч24
Linear equations (system), triangular form      9Ч10 23
Linear equations (system), two unknowns      4Ч6
Linear functional      397 426Ч427
Linear independence      43 147Ч149
Linear mapping      314Ч316 319 326Ч328
Linear mapping, image      316Ч319 328Ч331
Linear mapping, kernel      316Ч320 328Ч332
Linear mapping, matrix representation      351
Linear mapping, nullity      318Ч319
Linear mapping, rank      318Ч319
Linear mapping, transpose      400
Linear operator      322
Linear operator, adjoint      425
Linear operator, characteristic polynomial      349
Linear operator, determinant      349
Linear operator, inner product spaces      425
Linear operator, invertible      323
Linear operator, matrix representation      344
Linear operator, nilpotent      373
Linear span      145
Located vectors      46
LU factorization      109Ч111 130Ч133
Mappings (maps)      312Ч314 324Ч326
Mappings (maps), composition of      313
Mappings (maps), linear      314Ч316 326Ч328
Matrices      13Ч14 74Ч75
Matrices, augmented      78
Matrices, block      79Ч80 86
Matrices, change-of-basis      160 348 430
Matrices, change-of-variable      105Ч106
Matrices, coefficient      17 78
Matrices, companion      375
Matrices, complex      96Ч97
Matrices, diagonal      93Ч94
Matrices, diagonizable      280 298
Matrices, echelon      14
Matrices, equivalent      102
Matrices, invertible      92Ч93
Matrices, nonsingular      92Ч93
Matrices, normal      97
Matrices, similar      357Ч359
Matrices, square      89Ч90
Matrices, triangular      94
Matrix representation, adjoint operator      426
Matrix representation, bilinear form      410Ч411
Matrix representation, linear maps      344 351 363Ч365
Matrix representation, quadratic form      104
Matrix space      142
Minimum polynomial      289Ч291 301Ч303 351
Minkowski's inequality      45
Minor      252 255Ч256
Minor principle      256
Monic polynomial      282 446
Multilinearity      257Ч258
Multiplication of matrices      76Ч77
Multiplicity      285
Multiplicity, n-space      40
Nilpotent      373
Nondegenerate linear equations      3
Nonnegative semidefinite      413
Nonsingular linear maps      320
Nonsingular matrices      92- 93
Norm      44 57Ч59 203 219Ч220 238
Normal matrix      97
Normal operator      428 432
Normal vector      46
Normalizing      44
Normed vector spaces      219Ч221
Nullity      318Ч319
One-norm      219Ч220
One-to-one correspondence      314
One-to-one mapping      314
Onto mapping      314
Operations on linear maps      320Ч321
Operators      See Linear operators
Orthogonal basis      209
Orthogonal complement      207Ч208 226
Orthogonal matrix      95 216 429Ч430
Orthogonal operator      427Ч429 431Ч432
Orthogonal projections      433
Orthogonal sets      208Ч209 212
Orthogonality      43 226Ч229 280
Orthogonalization (Gram Ч Schmidt)      213
Orthonormal basis      209
1 2
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