- Page 1 and 2: Linear AlgebraJim Hefferon( 13)( 21
- Page 3: PrefaceThis book helps students to
- Page 7 and 8: ContentsChapter One: Linear Systems
- Page 9: 1 Definition and Examples . . . . .
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44 Chapter One. Linear Systemš 2.
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46 Chapter One. Linear SystemsIIIRe
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48 Chapter One. Linear Systemsof th
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50 Chapter One. Linear Systemsthis
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52 Chapter One. Linear Systems1.10
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54 Chapter One. Linear SystemsIn th
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56 Chapter One. Linear SystemsWe ca
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58 Chapter One. Linear SystemsSince
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60 Chapter One. Linear Systems(a)(
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62 Chapter One. Linear SystemsTopic
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64 Chapter One. Linear SystemsTopic
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66 Chapter One. Linear Systemsnext
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68 Chapter One. Linear SystemsTopic
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70 Chapter One. Linear Systemschip,
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72 Chapter One. Linear SystemsTopic
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74 Chapter One. Linear Systems↑ i
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76 Chapter One. Linear Systems2 In
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Chapter TwoVector SpacesThe first c
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section I. Definition of Vector Spa
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Section II. Linear Independence 101
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Section II. Linear Independence 103
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Section II. Linear Independence 105
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Section II. Linear Independence 107
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Section II. Linear Independence 109
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Section II. Linear Independence 111
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Section III. Basis and Dimension 11
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Section III. Basis and Dimension 11
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Section III. Basis and Dimension 11
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Section III. Basis and Dimension 11
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Section III. Basis and Dimension 12
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Section III. Basis and Dimension 12
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Section III. Basis and Dimension 12
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Section III. Basis and Dimension 12
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Section III. Basis and Dimension 12
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Section III. Basis and Dimension 13
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Section III. Basis and Dimension 13
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Section III. Basis and Dimension 13
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Section III. Basis and Dimension 13
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Section III. Basis and Dimension 13
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Topic: Fields 141We could develop L
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Topic: Crystals 143Another crystal
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Topic: Crystals 145(e) Find the len
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Topic: Dimensional Analysis 147arcr
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Topic: Dimensional Analysis 149Thus
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Topic: Dimensional Analysis 151quan
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Chapter ThreeMaps Between SpacesIIs
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Section I. Isomorphisms 1551.3 Defi
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Section I. Isomorphisms 157The map
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Section I. Isomorphisms 159vector s
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Section I. Isomorphisms 161̌ 1.17
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Section I. Isomorphisms 163I.2 Dime
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Section I. Isomorphisms 165(it is w
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Section I. Isomorphisms 167One way
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Section I. Isomorphisms 169(b) The
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Section II. Homomorphisms 1711.3 Ex
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Section II. Homomorphisms 173Proof.
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Section II. Homomorphisms 175We sta
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Section II. Homomorphisms 177(b) If
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Section II. Homomorphisms 179The pr
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Section II. Homomorphisms 181Again
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Section II. Homomorphisms 183Now fo
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Section II. Homomorphisms 1852.21 T
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Section II. Homomorphisms 187̌ 2.3
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section III. Computing Linear Maps
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Section IV. Matrix Operations 207Re
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Section IV. Matrix Operations 209IV
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Section IV. Matrix Operations 211Di
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Section IV. Matrix Operations 213Ex
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Section IV. Matrix Operations 215(b
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Section IV. Matrix Operations 217Af
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Section IV. Matrix Operations 219An
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Section IV. Matrix Operations 221To
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Section IV. Matrix Operations 223Ex
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Section IV. Matrix Operations 2253.
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Section IV. Matrix Operations 227He
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Section IV. Matrix Operations 2294.
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Section IV. Matrix Operations 2314.
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Section V. Change of Basis 2331.2 L
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Section V. Change of Basis 235Exerc
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Section V. Change of Basis 2372.1 E
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Section V. Change of Basis 239We ca
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Section V. Change of Basis 241All 2
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Section V. Change of Basis 243̌ 2.
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Section VI. Projection 2451.1 Defin
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Section VI. Projection 247The formu
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Section VI. Projection 249VI.2 Gram
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Section VI. Projection 251Again the
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Section VI. Projection 253) ( ) ( )
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Section VI. Projection 255To projec
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Section VI. Projection 257NMIn addi
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Section VI. Projection 259The final
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Section VI. Projection 2613.15 What
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Topic: Line of Best Fit 263Topic: L
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Topic: Line of Best Fit 265We close
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Topic: Line of Best Fit 267(b) Find
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Topic: Geometry of Linear Maps 269(
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Topic: Geometry of Linear Maps 271(
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Topic: Geometry of Linear Maps 273T
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Topic: Markov Chains 275Topic: Mark
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Topic: Markov Chains 2770 − 01
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Topic: Markov Chains 279(b) Startin
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Topic: Orthonormal Matrices 281Topi
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Topic: Orthonormal Matrices 283orth
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Topic: Orthonormal Matrices 285Alth
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Chapter FourDeterminantsIn the firs
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Section I. Definition 289determines
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Section I. Definition 291Exercises
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Section I. Definition 2931.18 Which
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Section I. Definition 2952.4 Exampl
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Section I. Definition 2972.20 Prove
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Section I. Definition 2993.3 Lemma
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Section I. Definition 301We can bri
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Section I. Definition 303(the secon
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Section I. Definition 3053.27 A mat
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Section I. Definition 307or with th
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Section I. Definition 309row swaps.
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Section I. Definition 311(terms wit
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Section II. Geometry of Determinant
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Section II. Geometry of Determinant
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Section II. Geometry of Determinant
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Section II. Geometry of Determinant
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Section III. Other Formulas 321The
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Section III. Other Formulas 3231.10
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Topic: Cramer’s Rule 325Topic: Cr
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Topic: Cramer’s Rule 3274 Suppose
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Topic: Speed of Calculating Determi
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ABCTopic: Projective Geometry 331To
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Topic: Projective Geometry 333Consi
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Topic: Projective Geometry 335to em
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Topic: Projective Geometry 337Note
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Topic: Projective Geometry 339for s
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Topic: Projective Geometry 341resul
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344 Chapter Five. SimilarityIn this
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346 Chapter Five. SimilarityI.2 Com
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348 Chapter Five. Similarity1.3 Exa
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350 Chapter Five. Similarityone sim
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352 Chapter Five. SimilarityIn the
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354 Chapter Five. Similarity3.3 Exa
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356 Chapter Five. Similarity3.8 Exa
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358 Chapter Five. SimilarityProof.
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360 Chapter Five. Similarity3.38 Do
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362 Chapter Five. Similarityhas thi
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364 Chapter Five. SimilarityExercis
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366 Chapter Five. Similarity2.5 Exa
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368 Chapter Five. Similaritystring
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370 Chapter Five. SimilarityFinally
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372 Chapter Five. Similaritythe nul
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374 Chapter Five. Similarity̌ 2.34
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376 Chapter Five. Similarity1.3 Def
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378 Chapter Five. Similarity1.8 The
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380 Chapter Five. Similarity1.12 Ex
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382 Chapter Five. Similarity(c) Dec
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384 Chapter Five. SimilaritySo the
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386 Chapter Five. SimilarityThe sec
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388 Chapter Five. Similarityon the
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390 Chapter Five. Similaritythe can
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392 Chapter Five. Similaritypower p
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394 Chapter Five. Similarity̌ 2.31
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396 Chapter Five. Similaritythen co
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398 Chapter Five. Similarity1968339
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400 Chapter Five. SimilarityKnowing
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402 Chapter Five. SimilarityIntrodu
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404 Chapter Five. SimilarityExercis
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406 Chapter Five. Similarityn 1 2 3
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408 Chapter Five. Similarity1099511
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A-2And. Consider the statement form
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A-4For all. The ‘for all’ prefi
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A-6possibilities: (i) if k + 1 is n
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A-8the union is P ∪ Q = {x ∣
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A-10sets must have the same number
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A-12We call each part of a partitio
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[Anton] Howard Anton, Elementary Li
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[Kemeny & Snell] John G. Kemeny, J.
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Indexaccuracyof Gauss’ method, 68
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full row rank, 130function, A-8inve
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similar, 318similarity, 347singular
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concatenation, 133set, A-7complemen