Linear Algebra Done Right · Problem 9C.11

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · determinants

Problem

Prove or give a counterexample: If F=R\mathbf{F} = \mathbf{R}, T∈L(V)T \in \mathcal{L}(V), and det⁡T>0\det T > 0, then TT has a square root. If F=C\mathbf{F} = \mathbf{C}, T∈L(V)T \in \mathcal{L}(V), and det⁡T≠0\det T \neq 0, then TT has a square root (see 8.41).

Related theory

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