Linear Algebra

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$MATLAB C++ Math Library Reference$

[Kemeny & Snell] John G. Kemeny, J. Laurie Snell, Finite Markov Chains, D.Van Nostrand, 1960. [Kemp] Franklin Kemp Linear Equations, American Mathematical Monthly, volume 89 number 8 (Oct. 1982), p. 608. [Knuth] Donald E. Knuth, The Art of Computer Programming, Addison Wesley, 1988. [Lang] Serge Lang, Linear Algebra, Addison-Wesley, 1966. [Leontief 1951] Wassily W. Leontief, Input-Output Economics, Scientific American, volume 185 number 4 (Oct. 1951), p. 15. [Leontief 1965] Wassily W. Leontief, The Structure of the U.S. Economy, Scientific American, volume 212 number 4 (Apr. 1965), p. 25. [Lieberman] David Lieberman, The Big Bucks Ad Battles Over TV’s Most Expensive Minutes, TVGuide,Jan.261991,p.11. [Macdonald & Ridge] Kenneth Macdonald, John Ridge, Social Mobility, in British Social Trends Since 1900, A.H. Halsey, Macmillian, 1988. [Macmillan Dictionary] William D. Halsey, Macmillan, 1979. [Math. Mag., Sept. 1952] Dewey Duncan (proposer), W. H. Quelch (solver), Mathematics Magazine, volume 26 number 1 (Sept-Oct. 1952), p. 48. [Math. Mag., Jan. 1957] M. S. Klamkin (proposer), Trickie T-27, Mathematics Magazine, volume 30 number 3 (Jan-Feb. 1957), p. 173. [Math. Mag., Jan. 1963, Q237] D. L. Silverman (proposer), C. W. Trigg (solver), Quickie 237, Mathematics Magazine, volume 36 number 1 (Jan. 1963). [Math. Mag., Jan. 1963, Q307] C. W. Trigg (proposer). Quickie 307, Mathematics Magazine, volume 36 number 1 (Jan. 1963), p. 77. [Math. Mag., Nov. 1967] Clarence C. Morrison (proposer), Quickie, Mathematics Magazine, volume 40 number 4 (Nov. 1967), p. 232. [Math. Mag., Jan. 1973] Marvin Bittinger (proposer), Quickie 578, Mathematics Magazine, volume 46 number 5 (Jan. 1973), p. 286, 296. [Munkres] James R. Munkres, Elementary Linear Algebra, Addison-Wesley, 1964. [Neimi & Riker] Richard G. Neimi, William H. Riker, The Choice of Voting Systems, Scientific American, June 1976, p. 21-27. [Nering] Evar D. Nering, Linear Algebra and Matrix Theory, second edition, John Wiley, 1970. [Niven & Zuckerman] I. Niven, H. Zuckerman, An Introduction to the Theory of Numbers, third edition, John Wiley, 1972. [Oakley & Baker] Cletus O. Oakley, Justine C. Baker, Least Squares and the 3:40 Mile, Mathematics Teacher, Apr. 1977. [Ohanian] Hans O’Hanian, Physics, volumeone,W.W.Norton,1985. [Onan] Onan, Linear Algebra. [Petersen] G. M. Petersen, Area of a Triangle, American Mathematical Monthly, volume 62 number 4 (Apr. 1955), p. 249. [Polya] G. Polya, Patterns of Plausible Inference,
[Programmer’s Ref.] Microsoft Programmers Reference. [Putnam, 1988, A-6] William Lowell Putnam Mathematical Competition, Problem A- 6, 1988, solution: American Mathematical Monthly, volume 96 number 8 (Oct. 1989), p. 688. [Putnam, 1990, A-5] William Lowell Putnam Mathematical Competition, Problem A- 5, 1990. [Rice] John R. Rice, Numerical Mathods, Software, and Analysis, second edition, Academic Press, 1993. [Rucker] Rudy Rucker, Infinity and the Mind, Birkhauser, 1982. [Ryan] Patrick J. Ryan, Euclidean and Non-Euclidean Geometry: an Analytic Approach, Cambridge University Press, 1986. [Seidenberg] A. Seidenberg, Lectures in Projective Geometry, Van Nostrand, 1962. [Smith] Larry Smith, Linear Algebra, second edition, Springer-Verlag, 1984. [Strang 93] Gilbert Strang The Fundamental Theorem of Linear Algebra, American Mathematical Monthly, Nov. 1993, p. 848-855. [Strang 80] Gilbert Strang, Linear Algebra and its Applications, second edition, Harcourt Brace Jovanovich, 1980. [Tan] Tan, Finite Mathematics. [Taylor] Alan D. Taylor, Mathematics and Politics: Strategy, Voting, Power, and Proof, Springer-Verlag, 1995. [Tilley] Burt Tilley, private communication, 1996. [Trono] Tony Trono, compiler, University of Vermont Mathematics Department High School Prize Examinations 1958-1991, mimeographed printing, 1991. [USSR Olympiad no. 174] The USSR Mathematics Olympiad, number 174. [Weston] J. D. Weston, Volume in Vector Spaces, American Mathematical Monthly, volume 66 number 7 (Aug./Sept. 1959), p. 575-577. [Weyl] Hermann Weyl, Symmetry, Princeton University Press, 1952. [Wickens] Thomas D. Wickens, Models for Behavior, W.H. Freeman, 1982. [Wilkinson 1965] Wilkinson, 1965 [Wohascum no. 2] The Wohascum County Problem Book problem number 2. [Wohascum no. 47] The Wohascum County Problem Book problem number 47. [Yaglom] I.M. Yaglom, Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century, translatedbySergeiSossinsky,Birkhäuser, 1988. [Zwicker] William S. Zwicker, The Voters’ Paradox, Spin, and the Borda Count, Mathematical Social Sciences, vol. 22 (1991), p. 187-227.
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Preface In most mathematics program
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dent projects for individuals or sm
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Contents 1 Linear Systems 1 1.I Sol
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5.II.1 Definition and Examples ....
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2 Chapter 1. Linear Systems To fini
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4 Chapter 1. Linear Systems Conside
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6 Chapter 1. Linear Systems the sec
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8 Chapter 1. Linear Systems Don’t
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12 Chapter 1. Linear Systems can al
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14 Chapter 1. Linear Systems Matric
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16 Chapter 1. Linear Systems Scalar
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18 Chapter 1. Linear Systems Must t
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20 Chapter 1. Linear Systems 2.30 [
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22 Chapter 1. Linear Systems Studyi
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24 Chapter 1. Linear Systems the bo
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26 Chapter 1. Linear Systems shows
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28 Chapter 1. Linear Systems 3.13 E
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30 Chapter 1. Linear Systems (a) 2x
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32 Chapter 1. Linear Systems 1.II L
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34 Chapter 1. Linear Systems positi
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36 Chapter 1. Linear Systems In R3
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38 Chapter 1. Linear Systems � 1.
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40 Chapter 1. Linear Systems Notice
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42 Chapter 1. Linear Systems 2.7 De
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44 Chapter 1. Linear Systems 2.25 P
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46 Chapter 1. Linear Systems We can
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48 Chapter 1. Linear Systems each e
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54 Chapter 1. Linear Systems x1 has
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56 Chapter 1. Linear Systems First,
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58 Chapter 1. Linear Systems 2.8 Ex
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60 Chapter 1. Linear Systems (2) Ca
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62 Chapter 1. Linear Systems (b) Th
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64 Chapter 1. Linear Systems For th
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66 Chapter 1. Linear Systems (a) Fi
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68 Chapter 1. Linear Systems 4 3 2
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70 Chapter 1. Linear Systems expert
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72 Chapter 1. Linear Systems Topic:
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74 Chapter 1. Linear Systems We beg
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76 Chapter 1. Linear Systems 1 Calc
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78 Chapter 1. Linear Systems parall
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80 Chapter 2. Vector Spaces 2.I Def
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82 Chapter 2. Vector Spaces For the
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84 Chapter 2. Vector Spaces A vecto
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86 Chapter 2. Vector Spaces 1.12 Ex
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88 Chapter 2. Vector Spaces Chapter
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90 Chapter 2. Vector Spaces (d) The
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92 Chapter 2. Vector Spaces 2.2 Exa
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94 Chapter 2. Vector Spaces second.
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96 Chapter 2. Vector Spaces Proof.
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98 Chapter 2. Vector Spaces The sub
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100 Chapter 2. Vector Spaces S. Mem
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102 Chapter 2. Vector Spaces 2.II L
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104 Chapter 2. Vector Spaces 1.5 Ex
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106 Chapter 2. Vector Spaces Lookin
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108 Chapter 2. Vector Spaces Proof.
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110 Chapter 2. Vector Spaces (a) {2
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112 Chapter 2. Vector Spaces � 1.
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114 Chapter 2. Vector Spaces 1.5 De
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116 Chapter 2. Vector Spaces 1.13 D
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118 Chapter 2. Vector Spaces � 1.
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120 Chapter 2. Vector Spaces we stu
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122 Chapter 2. Vector Spaces 2.11 C
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124 Chapter 2. Vector Spaces subspa
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126 Chapter 2. Vector Spaces 3.6 De
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128 Chapter 2. Vector Spaces Anothe
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130 Chapter 2. Vector Spaces (a)
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132 Chapter 2. Vector Spaces by fin
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134 Chapter 2. Vector Spaces has a
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136 Chapter 2. Vector Spaces 4.12 E
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138 Chapter 2. Vector Spaces 4.22 I
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140 Chapter 2. Vector Spaces (c) Le
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142 Chapter 2. Vector Spaces We cou
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144 Chapter 2. Vector Spaces Then w
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146 Chapter 2. Vector Spaces (d) Pl
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148 Chapter 2. Vector Spaces howeve
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150 Chapter 2. Vector Spaces positi
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152 Chapter 2. Vector Spaces Topic:
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154 Chapter 2. Vector Spaces The cl
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156 Chapter 2. Vector Spaces Remark
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158 Chapter 2. Vector Spaces (b) Sh
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160 Chapter 3. Maps Between Spaces
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Chapter 4 Determinants In the first
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Section I. Definition 295 determine
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Section I. Definition 297 Exercises
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Section I. Definition 299 1.15 Prov
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Section I. Definition 301 That resu
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Section I. Definition 303 (b) Prove
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Section I. Definition 305 3.2 Defin
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Section I. Definition 307 Therefore
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Section I. Definition 309 read alou
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Section I. Definition 311 � 3.23
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Section I. Definition 313 could be
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Section I. Definition 315 We still
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Section I. Definition 317 (terms wi
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Section II. Geometry of Determinant
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Section III. Other Formulas 327 The
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Section III. Other Formulas 329 1.9
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Topic: Cramer’s Rule 331 Topic: C
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Topic: Cramer’s Rule 333 4 Suppos
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Topic: Speed of Calculating Determi
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Topic: Projective Geometry 337 Topi
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Topic: Projective Geometry 339 P P
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Topic: Projective Geometry 341 of t
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Topic: Projective Geometry 343 The
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Topic: Projective Geometry 345 the
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Chapter 5 Similarity While studying
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Section I. Complex Vector Spaces 34
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Section II. Similarity 351 5.II Sim
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Section II. Similarity 353 1.7 Cons
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Section II. Similarity 355 2.4 Coro
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Section II. Similarity 357 2.12 The
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Section II. Similarity 359 and the
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Section II. Similarity 361 Proof. A
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Section II. Similarity 363 3.19 Cor
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Section III. Nilpotence 365 5.III N
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Section III. Nilpotence 367 and thi
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Section III. Nilpotence 369 Proof.
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Section III. Nilpotence 371 The new
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Section III. Nilpotence 373 Now, wi
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Section III. Nilpotence 375 We can
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Page 389 and 390: Section IV. Jordan Form 379 5.IV Jo
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Page 409 and 410: Topic: Computing Eigenvalues—the
Page 411 and 412: Topic: Computing Eigenvalues—the
Page 413 and 414: Topic: Stable Populations 403 Topic
Page 415 and 416: Topic: Linear Recurrences 405 Topic
Page 417 and 418: Topic: Linear Recurrences 407 And,
Page 419 and 420: Topic: Linear Recurrences 409 diamo
Page 421 and 422: Topic: Linear Recurrences 411 Compu
Page 423 and 424: Appendix Introduction Mathematics i
Page 425 and 426: A-3 ‘if a number is divisible by
Page 427 and 428: Techniques of Proof A-5 Induction.
Page 429 and 430: A-7 The Principle of Extensionality
Page 431 and 432: A-9 So an identity map plays the sa
Page 433 and 434: A-11 Similarly, the equivalence rel
Page 435 and 436: Bibliography [Abbot] Edwin Abbott,
Page 437: [Feller] William Feller, An Introdu
Page 441 and 442: congruent plane figures, 286 contra
Page 443 and 444: Gauss’ method, 3 Gauss-Jordan, 46
Page 445 and 446: educed echelon form, 46 reflection,
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Linear Algebra

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