Linear Algebra Done Right · Problem 5D.3

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · diagonalizable-operators

Problem

Suppose VV is finite-dimensional and T∈L(V)T \in \mathcal{L}(V). Prove that if the operator TT is diagonalizable, then V=null⁡T⊕range⁡TV = \operatorname{null} T \oplus \operatorname{range} T.

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