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Olver P.J., Shakiban C. — Applied linear. algebra
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Название: Applied linear. algebraАвторы: Olver P.J., Shakiban C. Аннотация: Applied mathematics rests on two central pillars: calculus and linear algebra. While calculus has its roots in the universal laws of Newtonian physics, linear algebra arises from a much more mundane issue: the need to solve simple systems of linear algebraic equations. Despite its humble origins, linear algebra ends up playing a comparably profound role in both applied and theoretical mathematics, as well as in all of science and engineering, computer science, probability and statistics, economics, numerical analysis, mathematical biology, and many other disciplines. Nowadays, a proper grounding in both calculus and linear algebra is an essential prerequisite for a successful career in science, engineering, and mathematics.
Язык: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 714Добавлена в каталог: 04.06.2011Операции: Положить на полку |
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Предметный указатель
Interest 511 513 514 Intermediate eigenvalue 424 Internal energy 300 617 618 Internal force 310 486 Internal motion 375 479 Internal power 309 Internet 510 Interpolant trigonometric 285 Interpolation 53 81 205 248 643 649 Interpolation, polynomial 201 630 Interpolation, spline 55 Interpolation, trigonometric 279 Intersection 65 88 interval 80 85 86 134 Invariant subspace 374 Inverse 31 33 39 41 42 51 73 344 394 Inverse discrete Fourier transform 281 Inverse elementary matrix 17 Inverse power method 571 Inverse, left 31 345 Inverse, right 31 345 Invertible 33 538 Irrational number 488 Irrotational 88 Isometry 360 Isotope 199 392 Isotope, radioactive 199 Iterates 511 Iterative method 562 Iterative system 514 516 Jacobi eigenvalue 560 Jacobi identity 11 343 485 Jacobi iteration matrix 550 Jacobi method 549 558 jagged 279 Java 14 Joint 122 312 Jordan Basis 439 457 515 523 Jordan Basis Theorem 439 Jordan block 402 440 441 478 523 Jordan canonical form 440 442 478 524 Jordan chain 438 456 469 474 522 Jordan chain solution 457 Jordan Matrix 441 442 Jump discontinuity 601 609 Kernel 107 116 118 125 272 366 414 Kirchhoff's current law 304 307 Kirchhoff's Voltage Law 303 Ky Fan norm 536 Laborer 544 Lag phase 503 Lagrange data 635 Lagrange multiplier 423 Lagrange polynomial 203 634 643 Laguerre polynomial 253 Language 391 Laplace equation 368 370 372 380 Laplace operator 380 Laplace transform 363 Laplacian 338 343 368 380 Largest eigenvalue 423 Laser printing 633 Lattice 545 Law of Cosines 140 Layer boundary 640 LDV factorization 43 Leading coefficient 367 Learning theory 391 Least squares 183 196 260 Least squares approximant 205 Least squares coefficient 263 Least squares error 201 209 214 265 430 Least squares solution 182 193 430 Leaves 517 Lebesgue integral 135 594 Left half plane 460 524 Left inverse 31 345 Left null space 115 272 Left-handed basis 105 237 Legendre function 636 Legendre polynomial 250 266 Leibniz rule 474 Length 131 132 letter 634 Level curve 465 Level set 465 Light cone 157 Light ray 180 LIMIT 595 596 598 603 Limit, continuum 585 588 589 609 613 Line 65 85 90 184 201 279 319 332 358 481 493 Line integral 125 Line segment 607 642 Line, stable 471 Line, tangent 314 331 481 Linear 331 Linear algebra 1 77 187 330 583 598 Linear algebraic system 546 Linear approximation 314 322 375 623 linear combination 89 97 103 451 Linear equation 2 Linear form 157 Linear function 330 331 332 338 353 363 378 382 612 Linear functional 597 Linear independence 174 Linear integral equation 364 Linear iterative system 511 515 Linear map 332 Linear motion 469 Linear operator 332 338 Linear ordinary differential equation 363 Linear ordinary differential operator 342 Linear programming 180 Linear superposition 446 451 607 Linear system 4 7 20 41 60 64 68 109 114 193 363 446 Linear system operation 2 23 38 Linear transformation 332 346 356 428 481 Linearity 2 Linearly dependent 95 97 98 Linearly independent 95 97 98 101 102 158 229 406 451 Local minimum 185 187 Logarithm 478 Loop 122 Low frequency 285 Lower Slobbovia 200 Lower triangular 4 16 40 45 554 Lowers trictly 16 lp 279 LU decomposition 42 LU factorization 18 71 240 541 Lucas number 521 Magic square 106 Magnitude 601 Main diagonal 8 44 53 Manufacturing 180 630 Map, difference 418 Map, linear 332 Map, perspective 361 363 Map, shift 401 418 Maple 14 58 Markov chain 540—542 Markov process 540 Mass 112 157 181 199 294 301 330 485 Mass matrix 384 499 Mass point 598 Mass-spring chain 294 300 304 310 485 487 499 504 507 585 588 Mass-spring ring 328 Mathematica 14 58 395 Mathematics applied 1 510 583 Mathematics financial 1 Mathieu boundary value problem 648 MATLAB 14 395 Matrix 4 79 332 444 530 612 Matrix addition 6 9 12 45 79 338 Matrix algebra 7 Matrix arithmetic 9 80 Matrix differential equation 472 Matrix exponential 473 476 477 481 483 Matrix factorization 562 Matrix multiplication 6 8 9 11 45 50 52 73 79 97 332 353 429 474 Matrix norm 476 531 534 536 Matrix polynomial 11 Matrix power 514 520 Matrix product 131 Matrix solution 472 473 Matrix, affine 360 Matrix, augmented 12 37 61 274 Matrix, banded 55 Matrix, bidiagonal 53 Matrix, block 12 52 Matrix, block diagonal 478 Matrix, circulant 418 Matrix, coefficient 5 7 24 107 446 511 546 641 Matrix, cofactor 114 Matrix, commuting 476 Matrix, complete 407 Matrix, conductance 303 Matrix, convergent 523 524 531 533 535 548 Matrix, covariance 160 430 Matrix, deflated 406 Matrix, diagonal 8 43 46 410 419 422 427 520 549 573 Matrix, elementary 16 17 39 74 350 Matrix, elementary reflection 244 352 404 Matrix, Gram 158 179 190 214 299 306 318 499 Matrix, Hilbert 58 59 161 215 266 557 567 Matrix, Householder 239 244 Matrix, identity 8 9 16 25 31 46 101 395 402 Matrix, improper orthogonal 237 Matrix, incidence 123 295 302—304 316 486 613 Matrix, interchange 25 Matrix, inverse 73 594 Matrix, Jordan 441 Matrix, Jordan block 402 478 Matrix, mass 384 499 Matrix, nonsingular 40 Matrix, orthogonal 235 241 348 360 405 418 572 573 Matrix, pentadiagonal 557 647 Matrix, permutation 25 28 33 43 60 72 Matrix, positive upper triangular 572 Matrix, projection 111 193 259 265 405 Matrix, proper orthogonal 237 420 482 Matrix, reduced incidence 295 296 306 320 325 499 Matrix, regular 14 18 43 46 71 164 541 576 Matrix, regular transition 541 Matrix, resistance 303 Matrix, resistivity 304 306 Matrix, rotation 35 347 Matrix, scaled incidence 586 Matrix, skew-symmetric 49 74 386 421 482 Matrix, sparse 50 53 Matrix, special lower triangular 17 18 28 40 43 46 60 165 576 Matrix, special upper triangular 38 43 Matrix, square 31 71 Matrix, stiffness 296 298 317 486 488 493 499 609 Matrix, strictly lower triangular 549 Matrix, symmetric 49 164 416 419 423 424 426 Matrix, transition 540 541 Matrix, tricirculant 55 Matrix, tridiagonal 53 296 405 527 578 632 644 Matrix, unitary 240 248 422 435 Matrix, upper Hessenberg 581 Matrix, upper triangular 71 241 248 435 572 576 Matrix, Vandermonde 20 75 201 206 208 Matrix, weight 211 Matrix, weighted Gram 212 Matrix, zero 8 9 63 79 Matrix-valued function 479 MAX 145 Maximization 183 423 Maximization principle 424 425 Maximum 150 Mean 10 86 Mean zero 86 592 Measure atomic 598 Measure theory 135 598 Measurement 196 Mechanics 181 390 421 Mechanics, classical 330 375 464 Mechanics, continuum 180 586 Mechanics, fluid 49 169 181 368 Mechanics, quantum 11 131 135 169 235 238 248 330 338 344 368 375 419 464 481 635 Mechanics, solid 181 Mechanism 321 325 481 492 493 495 Media digital 218 277 Medical image 104 Membrane 635 Memory 57 553 Mesh point 630 642 Methane molecule 140 Method, deflation 572 Method, direct 562 Method, inverse power 571 Method, iterative 562 Method, naive iterative 557 Method, power 568 575 Method, shifted inverse power 572 580 Metric 360 microwave 503 Midpoint rule 209 Minimal 328 Minimization 183 423 Minimization principle 300 388 563 617 621 622 639 640 Minimizer 188 387 563 Minimum 150 181 Minimum norm solution 275 Minimum, global 187 188 Minimum, local 185 Miningdata 391 429 Minkowski form 363 Minkowski space-time 157 Minkowski's inequality 145 Minneapolis 542 Minnesota 393 514 542 Missile 208 Mixed boundary value problem 614 622 636 Mode normal 488 Mode unstable 493 495 Mode vibrational 493 Modeling geometric 630 Modulate 501 Modulus 171 513 Molasses 499 Molecule 419 Molecule triatomic 494 496 509 Molecule water 497 509 moment 319 Moment bending 623 Moment of inertia 421 Momentum 330 344 money 511 513 514 Monic Legendre polynomial 249 Monitor 279 Monomial 91 100 103 261 Monomial sample vectors 262 Motion 313 Motion circular 493 Motion dynamical 486 Motion internal 375 479 Motion nonlinear 322 Motion rigid 318 320 325 360 481 492 493 495
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