Matriz 4x4
essa é a questão
essa é a resolução da questão 2
https://docs.google.com/document/d/1-7D6DBPOQSjtdBcRSpcEJvjzAiGm7oZo-mzZ5uDjLe8/edit
Polinômio Característico: [ 1. 3. -3. -11. -6.]
Autovalores: [ 2. -3. -1. -1.]
Autovetores:
Autovalor 2.000000000000001:
[ 0.5 -0.5 -0.5 0.5]
Autovalor -3.000000000000001:
[-3.01511345e-01 -9.04534034e-01 1.35122215e-16 3.01511345e-01]
Autovalor -1.0000000000000002:
[ 0.66679943 0.73119426 0.06439483 -0.12878967]
Autovalor -0.9999999999999981:
[-0.15795739 0.26717066 0.42512805 -0.8502561 ]
Rank dos Autovetores: 4
A matriz A é diagonalizável? True
Base Ortonormal:
[[ 0.5 -0.59160798 0.57338806 0.26688224]
[-0.5 -0.76063883 -0.1739157 -0.3757418 ]
[-0.5 0.25354628 0.79894472 -0.21771912]
[ 0.5 0.08451543 0.05164096 -0.86034316]]
Matriz P:
[[ 5.00000000e-01 -3.01511345e-01 6.66799429e-01 -1.57957386e-01]
[-5.00000000e-01 -9.04534034e-01 7.31194262e-01 2.67170665e-01]
[-5.00000000e-01 1.35122215e-16 6.43948330e-02 4.25128051e-01]
[ 5.00000000e-01 3.01511345e-01 -1.28789666e-01 -8.50256103e-01]]
Matriz P^{-1}:
[[ 0.66666667 -0.66666667 -2. -1.33333333]
[ 1.1055416 -1.1055416 3.31662479 1.1055416 ]
[ 1.62705857 -0.17930543 2.89550629 1.08914229]
[ 0.53762429 -0.7569178 -0.43858702 -1.73312911]]
Matriz P^{-1}AP:
[[ 2.00000000e+00 -1.03397092e-16 5.36046812e-16 -8.66011870e-16]
[-4.51119692e-15 -3.00000000e+00 6.04492230e-16 5.72604554e-16]
[-2.57330652e-15 1.36384794e-15 -1.00000000e+00 -6.62027823e-16]
[ 9.39943481e-16 5.23653002e-16 2.55075535e-17 -1.00000000e+00]]