A problem in Hoffman's Linear Algebra.

Page 243

18. If T is a diagonalizable linear operator, then every T-invariant subspace has a complementary T-invariant subspace. And vice versa.

In fact, the answer lies on Pages 263~265,but I try not to use the conception T-admissible to prove this proposition.

Could someone help me out?

Page 243

18. If T is a diagonalizable linear operator, then every T-invariant subspace has a complementary T-invariant subspace. And vice versa.

In fact, the answer lies on Pages 263~265,but I try not to use the conception T-admissible to prove this proposition.

Could someone help me out?

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