关于广义特征值的一个Wielandt型定理

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B??3WIQI?AB??3eA ?????_A?:?S???????4???!?C?????J?M??B???CA???:?S???????4???!.???:?????!B??3eIQ}?? B???CA???XWielandt?J?M???P }??1(P(B??3eA)??P(A?CB)?C(4) ???.????B???CA=IB??3eIQI}??B???C{Q}??!QI??A?C??Q?????E Q=e3e??DAD??3W?CD??diag(e???C?Ce3e??2?Cr??CP93e?.) ?I?C?J1?C?v?C?E??R 19?? 94 ???C(4)?E?????O?_???E?C?.??=P9?N(A?CB)?:Q????B???????Z?C?=Q?CB)??P(A?CB).???M????. 4.?????? ?????????Z?????X???????????B?c?c?z?P?C???????????M???M???????i?????Z???????? ???M???S?G???i.???????i?????Z?M?????????????Z?????h?????0???????.???????C?S???H?M ???E???C???H???X???Z. ???2???} [1PJWoods?CJ.E.?C?T????themat??aleconoP1ics[MPJ?CLongman?CLondon?C1978?C182??192?C243??253. [2]?K?????C?K?V???C???????![Mj?C?6???m?????K?f?C?n???C2001?C129??130?C239??257. PC3PJ?I?????C???!??[MPJ?C???n???i?m?????K?f?C?????C2001?C135??136?C385??386. [4PJ?????S?.???C???Z?M???B?????!??[MPJ?C???????K?f?C?n???C1986?C58??64. P.5]?????.???C???!?????J??[MPJ?C?F?????????:???K?f?C?F???C1983?C347??349. ??6PJ?e?????C?????????????Z?P???????=Gerschgorin?????MP.JPJ?C?????????C1994?C1:49??51. ??7PJ?e?????C?????????????Z?P????????????P.JPJ?C?????????C18:3(2001)?C88??90. A?;VIELANDT?CTHEOREMON GENERALIZEDEIGENVALUES Liuyi??hongXiongHui??jun (DePt.ofMdthematicsandll??PJr??ationscience?CChangshaUniversit?V?CChangsha?C410003?CChina) Abstractwielandt3Wslemmaisofmostusefulinestimatingandfindingcharacteristicva1uesofmatrices. ThispaperconcentratesongeneralizedeigenvalueproblemAx3d??xwhereAandBarespecialmatricesin economicanalysis.UsingthemethodsomewhatsimilartooneintheproofofWielandt3Wslemma?Cweprovea morecomplicatedwielandt3etheoremongeneralizedeigenvalues. KeywordsGeneralizedeigenvalue?Cnonnegativematrix?CM??matrix?Cirreduciblematrix?CWielandt3esLemma