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| Lipschutz Seymour — Schaum's Outline of Theory and Problems of Linear Algebra (Schaum's Outlines) |
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| Предметный указатель |
Outer product 49
P(t) 143
Parallelogram law 39
Parameters 4 10 47
permutations 249 269—272
Perpendicular 43
Pivot entries 16
Pivoting (row reduction) 27
Planes 61—65
Point 40 52
Polar form 412
Polynomial 446
Polynomial, characteristic 281—284
Polynomial, degree 446—447
Polynomial, Legendre 214
Polynomial, minimum 289—291 301—303 351
Polynomial, monic 446
Positive definite matrices 108 127—128 214—216
Positive definite operators 427
Positive operators 427
Powers of matrices 91
Primary decomposition 372
Principal minor 256
Product, cross 49—50
Product, dot 43—44 52
Product, inner 202—205 221—226
Projections 45—46 211—212 315 338 390—391 397 433
Projections, orthogonal 433
Pythagorean Theorem 209
Quadratic forms 104—108 124—127 289 298 300—301 412
Quadratic forms, diagonalizing 104
Quadratic forms, Hermitian 414
Quadratic forms, matrix representation 104
Quotient spaces 376—377 385—387
Rank 102 107 152
Rational canonical form 375—376
Re z 51
Real part 51
Real symmetric bilinear form 412—413
Reduction algorithm, determinants 252—253
Reduction algorithm, linear equations 11—12
Ring of polynomials 446
Row 13 74
Row, canonical form 14 16 28—30
Row, equivalence 14 98
Row, operations 14 98
Row, rank 152
Row, reducing 14 26—27
Row, space 146—147
Row, vector 75
scalar 40 141
Scalar matrix 91
Scalar product 43
Schwarz (Cauchy — Schwarz) inequality 45 58
Second dual space 399
Self-adjoint operator 427
Signature 102 107
Similarity, matrices 109 128—130 357—359
Similarity, operators 349
singular 320 332
Size of a matrix 13 74
| Skew-adjoint operator 427
Skew-Hermitian 97
Skew-symmetric 94 411
Solutions 1 21—23
Solutions, general 1 7
Solutions, simultaneous 5
span 145
Spanning sets 145
Spatial vectors 39 49 62—65
Spectral theorem 433
Square matrix 89—90 111
Square matrix, block 98 123—124
Square root of a matrix 285
Standard form 7
Sum of vector spaces 155—156
Surjective map 314
Sylvester's theorem 413
Symmetric bilinear form 411—412 416—418
Symmetric matrices 94—95
Symmetric matrices, congruent 102 124
Systems of linear equations See Linear equations
Tangent vector 48
Trace 90 349
Transition matrix 160 348
Transpose linear mapping 400
Transpose matrix 77 85
Triangle inequality 205
Triangular form, linear equations 9 23
Triangular form, linear operators 369 385 387—388
Triangular matrix 94
Triangular matrix, block 98
Two-norm 219
Unit vector 44 206
Unity matrix 97 430
Unity operator 427
Unknown, leading 3
Usual basis 150
Usual inner product 203 218
V* 397
V** 399
Variable, free 3
Vector 39 40
Vector space 141—142 162—163
Vector space, basis 150 169—170
Vector space, dimension 150—151 169—170
Vector space, normed 219
Vector space, sums 155—156
Vector, addition 41 52
Vector, column 75
Vector, coordinate 157—159 186—187
Vector, located 46
Vector, normal 46
Vector, row 75
Vector, scalar multiplication 41 52
Vector, spatial 39 49 62—65
Vector, tangent 48
Vector, unit 44 206
Vector, zero 41
Zero mapping 315
Zero matrix 76
Zero polynomial 441 446
Zero vector 41
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