Transcription of Basic Algebra - Mathematics and Statistics
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Basic Algebra - Mathematics and Statistics
Basic ,withanappendix ElementaryComplexAnalysis AdvancedRealAnalysisAnthony W. KnappBasic AlgebraAlong with a Companion VolumeAdvanced AlgebraDigital Second Edition, 2016 Published by the AuthorEast Setauket, New , aknappTitle:BasicAlgebraCover:Constructi onofaregularheptadecagon,thestepsshownin colorsequence; (2010):15 01,20 01,13 01,12 01,16 01,08 01,18A05, ,ISBN-13978-0-8176-3248-9c auserBostonDigitalSecondEdition,nottobes old,noISBNc ,images,andotherdatacontainedinthisfile, whichisinportabledocumentformat(PDF),are proprietarytotheauthor,andtheauthorretai nsallrights,includingcopyright, ,trademarks,servicemarks,andsimilaritems ,eveniftheyarenotidentifiedassuch, userBoston,c/oSpringerScience+BusinessMe diaInc.,233 SpringStreet,NewYork,NY10013,USA, ,scholarship,andresearch,andforthesepurp osesonly, ,postitonline,andtransmititdigitallyforp urposesofeducation,scholarship, ( ,EPUB),theymaynoteditit, ,usersmustchargenofee, ,noextractsorquotationsfromthisfilemaybe usedthatdonotconsistofwholepagesunlesspe rmissionhasbeengrantedbytheauthor(andbyB irkh userBostonifappropriate).
5. Row Reduction 19 6. Matrix Operations 24 7. Problems 30 II. VECTOR SPACES OVER Q, R, AND C 33 1. Spanning, Linear Independence, and Bases 33 2. Vector Spaces Defined by Matrices 38 3. Linear Maps 42 4. Dual Spaces 50 5. Quotients of Vector Spaces 54 6. Direct Sums and Direct Products of Vector Spaces 58 7. Determinants 65 8.
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