Linear Algebra Done Right · Problem 7C.2

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · positive-operators

Problem

Suppose T∈L(F4)T \in \mathcal{L}(\mathbf{F}^4) is the operator whose matrix (with respect to the standard basis) is (2−100−12−100−12−100−12).\begin{pmatrix} 2 & -1 & 0 & 0 \\ -1 & 2 & -1 & 0 \\ 0 & -1 & 2 & -1 \\ 0 & 0 & -1 & 2 \end{pmatrix}. Show that TT is an invertible positive operator.

Related theory

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