題組內容

5. Let V be a vector space of dimension 2. We say that a linear map $T: V \to V$ is self-adjoint if $\langle T(v), w \rangle = \langle v, T(w) \rangle$.

(1) Suppose that $\{v_1, v_2\}$ is an orthonormal basis for $V$ and $T: V \to V$ is a self-adjoint linear map. Show that the matrix of $T$ relative to that basis is symmetric. (15%)

題組內容

(1) Suppose that $\{v_1, v_2\}$ is an orthonormal basis for $V$ and $T: V \to V$ is a self-adjoint linear map. Show that the matrix of $T$ relative to that basis is symmetric. (15%)

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