Answer to Question #340393 in Linear Algebra for Lala

Question

Let T : V → V be a linear operator on a finite-dimensional vector space V over C such that T² = T.

7.1 Show that R(T) ⊆ N(T − I) and R(T − I) ⊆ N(T).

7.2 Show that V = R(T) + R(T − I).

7.3 Show that V = N(T) ⊕ N(T − I).

7.4 Show that T is diagonalisable

Answer 1

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