LinearAlgebra3.3.2PropertiesoftheLargestIndependentGroupsandRankQuestion3.Ifthevectorgroupitselfislinearlyindependent,whatisthelargestindependentgroupofthevectorgroup?Property1.AvectorgroupislinearindependentThenumberofvectorsitcontainsisequaltoitsrank.1=1002=,0103=001Conclusion1.I0:1,2,,rislinearlyindependent,thenthelargestindependentgroupofI0isitself.Forexample,in11,01,10,3=1=...
LinearAlgebra3.2.2PropertiesofLinearCorrelationofVectorGroupsTheorem6VectorgroupA:islinearlydependent,ÛTherankofthematrixA=()<m(thenumberofvectors).VectorgroupA:islinearlyindependent,ÛTherankofthematrixA=()=m(thenumberofvectors).Note:1)Theconclusionalsoholdsfortherowvectorcase.ExampleDeterminethelinearcorrelationofvectorgroupSolution:LetObviously,usingTheorem6todeterminethecorrelationisverysi...
LinearAlgebra3.1.2DefinitionandPropertiesofLinearCombinationandLinearRepresentation;andarecollinear.Geometry:Thereisauniquerealscalarksuchthat=kCalled:canbelinearlyrepresentedby.Geometry:k1k2=k1+k2andarenotcollinear;,andarecoplanarTherearerealscalarsk1、k2suchthat=k1+k2Called:canbelinearlyrepresentedby,DefinitionGivenavectorgroup,sca...
LinearAlgebra3.1.1VectorandLinearOperation)HorizontalAngleofFuselage:ElevationAngleofFuselage:AngleoftheWing:Todeterminethestatusoftheaircraft,a6-dimensionalvectorisrequired:Descriptionofaircraftflightstatus¿𝜽(𝟎≤𝜽<𝟐𝝅)𝝍(−𝝅<𝝍≤𝝅)𝝓(−𝝅𝟐≤𝝓≤𝝅𝟐)Todeterminethestatusoftheaircraft,thefollowing6parametersarerequired:Thepositionparametersofthefocusinspace:R:255G:255B:0R:255G:0B:255255...
TwoPropertiesofSVDandItsApplicationinDataHidingYun-xiaLiandHong-binZhangCollegeofComputerScience,BeijingUniversilyofTechnology,Beijing,Chinayunxiall6@gmail・com,zhanghbpr@gami1.comAbstract.Inthispaper,twonewPropertiesofsingularvaluedecomposition(SVD)onimagesareproved・Thefirstpropertydemonstrates(hequaniiiaiiverelationshipbetweensingularvaluesandpowerspecirum.Thesecondoneprovesthatunderthecondi...