LEADER 04890nam 2200613Ia 450 001 9910462642803321 005 20200520144314.0 010 $a1-61444-212-6 035 $a(CKB)2670000000418454 035 $a(EBL)3330448 035 $a(SSID)ssj0000577672 035 $a(PQKBManifestationID)11374574 035 $a(PQKBTitleCode)TC0000577672 035 $a(PQKBWorkID)10561914 035 $a(PQKB)10501473 035 $a(UkCbUP)CR9781614442127 035 $a(MiAaPQ)EBC3330448 035 $a(Au-PeEL)EBL3330448 035 $a(CaPaEBR)ebr10751045 035 $a(OCoLC)929120403 035 $a(EXLCZ)992670000000418454 100 $a19951031d1995 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLinear algebra problem book$b[electronic resource] /$fPaul R. Halmos 210 $a[Washington, DC] $cMathematical Association of America$dc1995 215 $a1 online resource (348 p.) 225 0 $aDolciani mathematical expositions ;$vno. 16 300 $aDescription based upon print version of record. 311 $a0-88385-322-1 327 $a""Linear Algebra Problem Book""; ""copyright page ""; ""Preface ""; ""Contents""; ""1 SCALARS""; ""1. Double addition""; ""2. Half double addition""; ""3. Exponentiation""; ""4. Complex numbers""; ""5. Affine transformations""; ""6. Matrix multiplication""; ""7. Modular multiplication""; ""8. Small operations""; ""9. Identity elements""; ""10. Complex inverses""; ""11. Affine inverses""; ""12. Matrix inverses""; ""13. Abelian groups""; ""14. Groups""; ""15. Independent group axioms""; ""16. Fields""; ""17. Addition and multiplication in fields""; ""18. Distributive failure"" 327 $a""19. Finite fields""""2 VECTORS""; ""20. Vector spaces""; ""21. Examples""; ""22. Linear combinations""; ""23. Subspaces""; ""24. Unions of subspaces""; ""25. Spans""; ""26. Equalities of spans""; ""27. Some special spans""; ""28. Sums of subspaces""; ""29. Distributive subspaces""; ""30. Total sets""; ""31. Dependence""; ""32. Independence""; ""3 BASES""; ""33. Exchanging bases""; ""34. Simultaneous complements""; ""35. Examples of independence""; ""36. Independence over R and Q""; ""37. Independence in C^2""; ""38. Vectors common to different bases""; ""39. Bases in C^3"" 327 $a""40. Maximal independent sets""""41. Complex as real""; ""42. Subspaces of full dimension""; ""43. Extended bases""; ""44. Finite-dimensional subspaces""; ""45. Minimal total sets""; ""46. Existence of minimal total sets""; ""47. Infinitely total sets""; ""48. Relatively independent sets""; ""49. Number of bases in a finite vector space""; ""50. Direct sums""; ""51. Quotient spaces""; ""52. Dimension of a quotient space""; ""53. Additivity of dimension""; ""4 TRANSFORMATIONS""; ""54. Linear transformations""; ""55. Domain and range""; ""56. Kernel""; ""57. Composition"" 327 $a""78. Reflexivity""""79. Annihilators""; ""80. Double annihilators""; ""81. Adjoints""; ""82. Adjoints of projections""; ""83. Matrices of adjoints""; ""6 SIMILARITY""; ""84. Change of basis: vectors""; ""85. Change of basis: coordinates""; ""86. Similarity: transformations""; ""87. Similarity: matrices""; ""88. Inherited similarity""; ""89. Similarity: real and complex""; ""90. Rank and nullity""; ""91. Similarity and rank""; ""92. Similarity of transposes""; ""93. Ranks of sums""; ""94. Ranks of products""; ""95. Nullities of sums and products""; ""96. Some similarities"" 327 $a""97. Equivalence"" 330 $aLinear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebra—and nowadays that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer. 410 0$aDolciani Mathematical Expositions 606 $aAlgebras, Linear 606 $aAlgebras, Linear$vProblems, exercises, etc 608 $aElectronic books. 615 0$aAlgebras, Linear. 615 0$aAlgebras, Linear 676 $a512/.5/076 700 $aHalmos$b Paul R$g(Paul Richard),$f1916-2006.$022815 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462642803321 996 $aLinear algebra problem book$91948760 997 $aUNINA