▁respect s : ▁they ▁can ▁be ▁ordered ▁( though ▁not ▁totally ▁ordered ), ▁they ▁are ▁complete , ▁all ▁their ▁eigenvalues ▁are ▁real ▁and ▁they ▁form ▁a ▁real ▁associ ative ▁algebra . ▁Pos itive - defin ite ▁operators ▁correspond ▁to ▁the ▁positive ▁re als ▁and ▁normal ▁operators ▁correspond ▁to ▁the ▁complex ▁numbers . ▁ ▁See ▁also ▁▁▁ ▁Cont in ued ▁fraction ▁ ▁Real ▁analysis ▁ ▁Notes ▁ ▁References ▁ ▁Cit ations ▁ ▁S ources ▁▁▁ ▁Cant or , ▁Georg ▁( 1 8 7 4 ). ▁" ". ▁, ▁volume ▁ 7 7 , ▁pp .   2 5 8 – 6 2 . ▁ ▁Fe fer man , ▁Sol omon ▁( 1 9 8 9 ). ▁The ▁Number ▁Systems : ▁Found ations ▁of ▁Al gebra ▁and ▁Analysis , ▁A MS ▁Ch else a , ▁. ▁ ▁K atz , ▁Robert ▁( 1 9 6 4 ). ▁A xi om atic ▁Analysis , ▁D . C . ▁He ath ▁and ▁Company . ▁ ▁Land au , ▁Edmund ▁( 2 0 0 1 ). ▁Found ations ▁of ▁Analysis . ▁American ▁Mathemat ical ▁Society ,. ▁ ▁How ie , ▁John ▁M . ▁Real ▁Analysis . ▁Springer , ▁ 2 0 0 5 , ▁. ▁ ▁. ▁ ▁External ▁links ▁▁▁▁ ▁The ▁real ▁numbers : ▁P yth ag or as ▁to ▁Ste vin ▁ ▁The ▁real ▁numbers : ▁Ste vin ▁to ▁Hil bert ▁ ▁The ▁real ▁numbers : ▁Att empt s ▁to ▁understand ▁ ▁What ▁are ▁the ▁" real ▁numbers ," ▁really ? ▁▁▁ ▁Category : Real ▁algebraic