3.4.1TheDefinitionofVectorSpaceLinearAlgebraDefinition(VectorSpace)Avectorsetiscalledavectorspaceifithas𝑉thefollowingthreeproperties.Vectorsetisnotempty𝑉(closedundervectoraddition)Ifandbelongto,belongstoV𝑉(closedundervectoraddition)Ifbelongstoandisascalar,belongstoV𝑉2)TheDefinitionalsospecifiesstepstoverifywhetheravectorsetisavectorspace:①Visnotempty;②Visclosedundervectoraddition;③...
LinearAlgebra3.3.1DefinitionofTheLargestIndependentGroupandRankofVectorGroupsR:255G:255B:0R:255G:0B:255R:0G:255B:2552550RedGreenBlue002552550002550Thepracticalmeaningofn-dimensionalvectorswhereVisiblecolorsinnaturecanbeobtainedbymixingprimarycolorswithcertainproportions,thatis,anycolorisregardedasalinearcombinationofred,greenandbluecolorvectors.Theprimarycolorsshouldbeindependenttoeachother,tha...
LinearAlgebra3.2.1DefinitionofLinearDependentofVectorGroupsandarecollinearGeometry:Thereisauniquerealscalark,suchthat=kTherearerealscalarssuchthat.Geometry:𝑘2¿𝑘1+𝑘2andarenotcollinear;and,arecoplanar.TherearerealscalarssuchthatTherearerealscalarssuchthatDefinitionVectorgroupislinearlydependent,iftherearescalarsthatarenotallzero,suchthatOtherwise,itisca...
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...
DefinitionDefinitionWarm-upActivityWhat’stheDefinitionof“pride”inadictionary?Is“pride”apositiveornegativeconception?Whatdoyouthinkoftheconceptof“pride”?Canyoucitesomeexamples?Whatcanyouconcludeabout“pride”?Introduction•WhatisDefinition?Definitionmeansestablishinglimitsormarkingboundariesofasubject.•WhydoweneedDefinitioninourcommunication?ByusingDefinition,wecanavoidconfusio...