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 $\langle T(v), w \rangle = \langle v, T(w) \rangle$.

(2) Assume that $f: V \times V \to R$ is a map defined by $f(v, w) = \langle T(v), w \rangle$ where $T$ is a self-adjoint linear map. Show that $f$ is a bilinear symmetric form of $V$. (15%)

題組內容

(2) Assume that $f: V \times V \to R$ is a map defined by $f(v, w) = \langle T(v), w \rangle$ where $T$ is a self-adjoint linear map. Show that $f$ is a bilinear symmetric form of $V$. (15%)

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