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LinearAlgebra3.3.2PropertiesoftheLargestIndependentGroupsandRankQuestion3.Ifthevectorgroupitselfislinearlyindependent,whatisthelargestindependentgroupofthevectorgroup?Property1.AvectorgroupislinearindependentThenumberofvectorsitcontainsisequaltoitsrank.1=1002=,0103=001Conclusion1.I0:1,2,,rislinearlyindependent,thenthelargestindependentgroupofI0isitself.Forexample,in11,01,10,3=1=... 2024-06-080471.4 KB11页
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3.4.3TransitionmatrixLinearAlgebraDefinitionIfandaretwobasesofthevectorspace,and𝑉.Denote𝑃thetransitionmatrixfrombasistobasis.basistransformationformula(𝛽1,𝛽2,⋯,𝛽𝑛)=(𝛼1,𝛼2,⋯,𝛼𝑛)𝑃ExampleThetransitionmatrixfrombasistobasisofis.(23−1−2)Solution:Giventhetransitionmatrix,𝑃(𝛼1,𝛼2)𝑃=(𝛽1,𝛽2).⇒𝑃=¿¿(110−1)−1(1112)¿(110−1)(1112)¿(23−1−2).ExampleSupposeProofthatisabasisofandf... 2024-06-080311.67 KB6页
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