矩阵的特征值与特征向量专题讲解

不排除由于是进行产品质量评审时,在项目的设置、抽样方法与质量检验的严谨程度上,都尚存在一定的问题；所以产品评审的过程需要进一步改进；以便更真实地反映情况出产品的真实问题；从而更全面、更本质地反映产品质量存在的问题与真实水平centerpinchecksandanchoringtheinnercylinder.AccordingtoWhilecouplingalignmentshouldkeepoiloutofcavityandlocatetherotoraxisneckraisedarewithintheprescribedlimits,thereshouldbenogaps,Horn,HornandHorn0.05mmfeelergaugesfitinto.Centercoupling,condenserwaterfillingandwater-filledaccordingtofactoryrequirement.ForcouplingthreesupportedrotorCenter,themouthunderthecouplingbetweenthevalueshouldbeasstipulatedinthemanufacturer,usually0.15~0.25mm.Inthecaseofcouplingconnection,ifpossible,liftingonlyonebearingendofthesupportbearingoftherotor,removethebearing,fittedwithspecialtilesandspecialliftingtools,discrotors,checkthejournalfluttertile,shouldgenerallybelessthan0.10MM.Whenthecouplingsandrotorcomeswhenthereisaconflict,thecouplingCentreshallprevail.6.4.5.2.2shaftlookingfor:...6.4.5.3.Provisionalboltconfirmedthepositioningoftherotorsize,aswellasthecouplingbetweentheadjustmentshimthicknessaccuracy,drawingstomeetthetechnicalrequirements.Plane,cylindricalandcleanthecouplingboltholesshouldbecleanandwithoutburrs,scrapironandgrease-free,relativepositionofthecouplingaccordingtothedrawingrequirementsare.Couplingtopscrews,rounddistanceapart,indicatorstomonitormovementoftheaircraft,itsvalueisallowedtopassthevalueaxismoving,mountedadjustmentpads,notepadsinstallationdirectionguidepincouplingwithprocessendclosed.Thebackwheelsslowlytightened,when2mmorso,withstandardwhitebarswheretwobackwheelboltholemeasurementaboveandbelow,confirmtwobackwheelboltholeconcentricity.Then,thesymmetricalhorizontalmounttwotemporaryboltstightened,attentiontomonitordialindicator,theninstallthesymmetricaltemporarybolts,thistimesitesslowlymovingrotor,inthemeasuredcircumferenceof8equalpartsbackwheelrimrock,eachmeasuringrelativechangesinvalueshouldbelessthan0.02mm.6.4.5.4couplingreamedandpairedboltreamingdiereamer,adjustablereamers,boringmill,inseveralways.6.4.5.4.1Generalrequirementsbeforereamingorboring,矩阵的特征值与特征向量专题讲解一、内容提要一、矩阵的特征值和特征向量1、基本概念设A为n阶方阵，若存在数和n为非零向量0,a使Aaa，则称是A的特征值，a是属于的特征向量；矩阵EA称为A的特征矩阵；EA是的n次多项式，称为A的特征多项式；EA=0称为A的特征方程；2、特征值、特征向量的求法（1）计算A的特征值，即解特征方程EA=0；（2）对每一个特征值0，求出相应的齐次线性方程组00EAX一个基础解系123,，，...,则属于0的全部特征向量为11...sskk，其中1,...,skk为不全为零的任意常数；3、特征值、特征向量的性质（1）A与TA的特征值相同（但特征向量一般不同）；（2）属于同一特征值的特征向量的线性组合仍是属于该特征值的特征向量；（3）属于不同特征值的特征向量线性无关；（4）设0Aaaa，则,,mkAAPA的特征值分别为,,mkP，其中Px为任一多项式，而a仍为相应的特征向量；（5）若A可逆，0Aaaa，则1是1A的特征值；A是*A的特征值，a仍为相应的特征向量；（6）设12n，，...是n阶方阵的特征值，则有11nniiiiiatrA（迹）；1niiA;推论：A可逆当且仅当A的特征值全不为零；（7）若A为实对称阵，则A的所有特征值均为实数，且属于不同特征值的特征向量彼此正交。二、相似矩阵不排除由于是进行产品质量评审时,在项目的设置、抽样方法与质量检验的严谨程度上,都尚存在一定的问题；所以产品评审的过程需要进一步改进；以便更真实地反映情况出产品的真实问题；从而更全面、更本质地反映产品质量存在的问题与真实水平centerpinchecksandanchoringtheinnercylinder.AccordingtoWhilecouplingalignmentshouldkeepoiloutofcavityandlocatetherotoraxisneckraisedarewithintheprescribedlimits,thereshouldbenogaps,Horn,HornandHorn0.05mmfeelergaugesfitinto.Centercoupling,condenserwaterfillingandwater-filledaccordingtofactoryrequirement.ForcouplingthreesupportedrotorCenter,themouthunderthecouplingbetweenthevalueshouldbeasstipulatedinthemanufacturer,usually0.15~0.25mm.Inthecaseofcouplingconnection,ifpossible,liftingonlyonebearingendofthesupportbearingoftherotor,removethebearing,fittedwithspecialtilesandspecialliftingtools,discrotors,checkthejournalfluttertile,shouldgenerallybelessthan0.10MM.Whenthecouplingsandrotorcomeswhenthereisaconflict,thecouplingCentreshallprevail.6.4.5.2.2shaftlookingfor:...6.4.5.3.Provisionalboltconfirmedthepositioningoftherotorsize,aswellasthecouplingbetweentheadjustmentshimthicknessaccuracy,drawingstomeetthetechnicalrequirements.Plane,cylindricalandcleanthecouplingboltholesshouldbecleanandwithoutburrs,scrapironandgrease-free,relativepositionofthecouplingaccordingtothedrawingrequirementsare.Couplingtopscrews,rounddistanceapart,indicatorstomonitormovementoftheaircraft,itsvalueisallowedtopassthevalueaxismoving,mountedadjustmentpads,notepadsinstallationdirectionguidepincouplingwithprocessendclosed.Thebackwheelsslowlytightened,when2mmorso,withstandardwhitebarswheretwobackwheelboltholemeasurementaboveandbelow,confirmtwobackwheelboltholeconcentricity.Then,thesymmetricalhorizontalmounttwotemporaryboltstightened,attentiontomonitordialindicator,theninstallthesymmetricaltemporarybolts,thistimesitesslowlymovingrotor,inthemeasuredcircumferenceof8equalpartsbackwheelrimrock,eachmeasuringrelativechangesinvalueshouldbelessthan0.02mm.6.4.5.4couplingreamedandpairedboltreamingdiereamer,adjustablereamers,boringmill,inseveralways.6.4.5.4.1Generalrequirementsbeforereamingorboring,1、定义设,AB为n阶方阵，若存在n阶可逆阵P，使1PAPB,称A与B相似，记为A～B；２、A～B的性质TTAB,,,MMkAkBAB～～～,PAPB～其中P为任一多项式；,,,rArBABEAEB特征值相同，trAtrB；若A可逆，则B也可逆，且11AB～。三、矩阵对角化的条件及方法１、若矩阵A与对角阵相似，则称A可对角化，（１）n阶方阵A可对角化的充分必要条件是A有n个线性无关的特征向量；（２）若A的特征值两两不同，则必可对角化。２、实对称阵A必可对角化，且存在正交阵P，使1PAP实对称矩阵正交对角化具体计算步骤如下：（１）求出实对称矩阵A的全部特征值；（２）若特征值是单根，则求出一个线性无关的特征向量，并加以单位化；若特征值是重根，则求出重数个线性无关的特征向量，然后用施密特正交化方法化为正交组，再单位化；