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



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

Àâòîð: Lipschutz Seymour

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/Àëãåáðà/Ëèíåéíàÿ àëãåáðà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1991

Êîëè÷åñòâî ñòðàíèö: 368

Äîáàâëåíà â êàòàëîã: 14.05.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$C^n$      52—53 72
$K^n$      142
$R^n$      40—41 53—54
Absolute value      52
Adjoint operator      425—426 433—436
Adjoint operator, matrix representation      426
Adjoint, classical      253—254
Algebra of linear maps      322
Algebraic multiplicity      285
Algorithm, basis-finding      154
Algorithm, determinant      253
Algorithm, diagonalization under, congruence      102—104
Algorithm, diagonalization under, similarity      102 286
Algorithm, Elimination (Gaussian)      8 24—25 100 261
Algorithm, Euclidean      446
Algorithm, Gauss — Jordan      29
Algorithm, inverse matrix      100
Algorithm, orthogonal diagonalization      289
Alternating bilinear form      411
angle      45 206
Annihilators      399—400 403—404
Arbitrary permutations      249
Augmented matrix      78
A{V)      322
B(V)      409
Back-substitution      9
Basis, dual      398 400—403
Basis, general solution      19—20
Basis, orthogonal      208
Basis, second dual      399
Basis, usual      150
Basis, vector space      150 169—171
Basis-finding algorithm      154
Bessel inequality      212
Bijective mapping      314
Bilinear form      409 414—416
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      412—413
Bilinear form, symmetric      411—412
Block matrix      79—80 86
Block matrix, determinant of      256—257
Block matrix, diagonal      98 291
Block matrix, Jordan      374
Block matrix, square      98 123—124
Block matrix, triangular      98
Cancellation law      142
Canonical form      14 352
Canonical form, Jordan      373—374 381—385
Canonical form, rational      375—376 388—390
Canonical form, row      14 16 28—30
Cauchy — Schwarz inequality      45 58 205—206 218
Cayley Hamilton theorem      282 302—304 307
cells      79
Change of basis      159—162 187—191
Change-of-basis matrix      160 348 357—359
Change-of-variable matrix      105—106
Characteristic polynomial      281—284 349
Classical adjoint      253—254
Codomain      312
Coefficient      1
Coefficient matrix      17 78
Coefficient, Fourier      211
Cofactor      252
column      13 74
Column, operations      100—102
Column, rank      152
Column, space      146
Column, vector      40 75
Commuting matrices      90
Companion matrix      291 375
Complement, orthogonal      207—208 226
Complex, conjugate      51
Complex, inner product      216—218
Complex, matrix      96 121—122
Complex, n-space      52
Complex, numbers      51
Component      40 211
Composition of mappings      313
Congruent, diagonalization      102—103
Congruent, matrices      102 410
Congruent, symmetric matrices      102—103 124—125
Conjugate matrix      96
Conjugate, complex      51
Consistent systems      13
Convex set      342 407
Coordinate vector      157 186—187
coordinates      40 157—159
cosets      376
Cramer's rule      255 263—264 268
Cross product      49—50 65—67
CURVES      48
Cyclic subspaces      374—375 388—389
Degenerate linear equations      2 3
Degree of polynomial      446
Dependence, linear      147 166—169
Determinant      246
Determinant, block matrix      256—257
Determinant, computation of      253 260—262
Determinant, linear equations      254—255
Determinant, linear operators      349
Determinant, multiplinearity      257—258
Determinant, order      3 248
Determinant, order n      250
Determinant, properties      251—252
Determinant, volume      257
Diagonal (of a matrix)      90
Diagonal matrix      93—94
Diagonal matrix, block      98
Diagonalizable matrices      280 288—289 298—301
Diagonalization      349—350 360—363
Diagonalization algorithm      102—104 286—288
Dimension of solution spaces      19
Dimension of vector spaces      150—151
Dimension of vector spaces, subspaces      151 171—172
Direct sum      156 181—186
Direct sum, decomposition      371 379—380
Directed line segment      46
Distance      45
Domain      312
Dot product      43—46 52 56—57
Dual basis      398
Dual space      397
Echelon form      10—11 14 23—24
Echelon matrices      14
Eigenvalue      284—285 292—298 350
Eigenvalue, computing      286—287
Eigenvector      284—286 292—298 350
Eigenvector, computing      286—287
Elementary divisors      376
Elementary matrix      99 101 117—118
Elementary operations      7—8
Elementary operations, column      100—102
Elementary operations, row      14 98—100
Elimination algorithm      6
Elimination, Gaussian      8 24—26 100 261
Enenspace      284 350
Equal matrices      74
Equal vectors      40
Equations      See Linear equations
Equivalence, matric      100 102
Equivalence, row      14 16
Equivalent systems      7—8
Euclidean algorithm      446
Euclidean space      203
Evaluation map      92
Factorization, LU      109—111 130—133
Factorization, polynomial      448
Field      74
Finite dimension      150—151
Fourier coefficient      211
Free variable      3 10
Function, spaces      143
Function, square matrix      89—90
Functional, linear      397
F{X)      143
Gauss — Jordan algorithm      29
Gaussian elimination      8 24—26 100 261
General solution      1 7
Geometric multiplicity      285
Gram — Schmidt orthogonalization      213
Graph      4
Greatest common divisor      447
Hermitian form      413—414
Hermitian matrix      97
Hermitian quadratic form      414
Hilbert space      205
Homogeneous systems      18—20 32—34 399—400
Hyperplane      46 407
Identity mapping      314
Identity matrix      91
ijk notation      49
Im F      316
Im z      51
Image of linear mapping      316—318 328—331
Imaginary part      51
Inconsistent systems      13
Independence, linear      147—150
Infinite dimension      150
Infinity-norm      219
Injective mapping      314
Inner product      202 221—226
Inner product spaces      202—205
Inner product spaces, linear operators on      425
Inner product, complex      216—218
Inner product, usual      203 214—216 218
Invariance      370—371
Invariant subspaces      370—371 377—378
Inverse matrix      92
Inverse matrix, computing algorithm      100
Invertible matrices      92—93 115—117
Invertible matrices, linear substitutions      105
Invertible matrices, operators      323
Isomorphic vector spaces      316
Isomorphism      158—159 316 320
Jordan block      374
Jordan canonical form      373—374
Ker F      316
Kernel of a linear map      316—320 328—332
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 41—42 145—147 149 165—166
Linear dependence      42—43 147—149 166—169
Linear equation      1
Linear equation, degenerate      2—3
Linear equation, one unknown      2
Linear equations (system)      1 21 152—153 319—320 323—324 399—400
Linear equations (system), consistent      13
Linear equations (system), echelon form      10 23—24
Linear equations (system), triangular form      9—10 23
Linear equations (system), two unknowns      4—6
Linear functional      397 426—427
Linear independence      43 147—149
Linear mapping      314—316 319 326—328
Linear mapping, image      316—319 328—331
Linear mapping, kernel      316—320 328—332
Linear mapping, matrix representation      351
Linear mapping, nullity      318—319
Linear mapping, rank      318—319
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      109—111 130—133
Mappings (maps)      312—314 324—326
Mappings (maps), composition of      313
Mappings (maps), linear      314—316 326—328
Matrices      13—14 74—75
Matrices, augmented      78
Matrices, block      79—80 86
Matrices, change-of-basis      160 348 430
Matrices, change-of-variable      105—106
Matrices, coefficient      17 78
Matrices, companion      375
Matrices, complex      96—97
Matrices, diagonal      93—94
Matrices, diagonizable      280 298
Matrices, echelon      14
Matrices, equivalent      102
Matrices, invertible      92—93
Matrices, nonsingular      92—93
Matrices, normal      97
Matrices, similar      357—359
Matrices, square      89—90
Matrices, triangular      94
Matrix representation, adjoint operator      426
Matrix representation, bilinear form      410—411
Matrix representation, linear maps      344 351 363—365
Matrix representation, quadratic form      104
Matrix space      142
Minimum polynomial      289—291 301—303 351
Minkowski's inequality      45
Minor      252 255—256
Minor principle      256
Monic polynomial      282 446
Multilinearity      257—258
Multiplication of matrices      76—77
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 57—59 203 219—220 238
Normal matrix      97
Normal operator      428 432
Normal vector      46
Normalizing      44
Normed vector spaces      219—221
Nullity      318—319
One-norm      219—220
One-to-one correspondence      314
One-to-one mapping      314
Onto mapping      314
Operations on linear maps      320—321
Operators      See Linear operators
Orthogonal basis      209
Orthogonal complement      207—208 226
Orthogonal matrix      95 216 429—430
Orthogonal operator      427—429 431—432
Orthogonal projections      433
Orthogonal sets      208—209 212
Orthogonality      43 226—229 280
Orthogonalization (Gram — Schmidt)      213
Orthonormal basis      209
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