《理工科代数基础》第五章 矩阵的 Jordan标准形

PAP=J,→P(-2)P=(J-2) r(A-2)=r(J-21),k=1,2, A-21 0204 0 0000 r(A-21)=2 20 02 10 r(A-2I)2=r 0000 =1

6 1 1 , ( 2 ) ( 2 ) , k k P AP J P A I P J I − − =  − = − ( 2 ) ( 2 ) , 1,2, k k  − = − = r A I r J I k 0 1 0 0 2 0 1 0 2 0 2 0 0 4 0 2 0 A I     − =    −      2 2 0 1 0 0 0 0 0 ( 2 ) 4 0 2 0 0 0 0 0 r A I r     − =   − −      r A I ( 2 ) 2 − = = 1

r(J-21)2=1 01 01 r(1-2D)2=r( 00 2 01 7(J2-21 0 0

7 2 1 0 1 0 1 ( 2 ) ( 0 0 0 r J I r     − =         2 )=1， 2 2 0 1 0 ( 2 ) ( 0 1 0 r J I r     − =         2 )=0， 2  − = r J I ( 2 ) 1