Question
Let $A=A^T$ be a real symmetric $n \times n$ matrix. Show that $(A \mathbf{v}) \cdot \mathbf{w}=\mathbf{v} \cdot(A \mathbf{w})$ for all $\mathbf{v}, \mathbf{w} \in \mathbb{C}^n$.
Step 1
The dot product is defined as: \[ \mathbf{v} \cdot \mathbf{w} = \sum_{i=1}^n v_i \overline{w_i}, \] where $\overline{w_i}$ denotes the complex conjugate of $w_i$. Show more…
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