I need to show that $a(u_{h},u_{h}) = u^{T}Au$ where $A$ is a symmetric $n \times n$ matrix and $a(u_{h},u_{h}) = ( \bigtriangledown u_{h},\bigtriangledown u_{h} ) = \int_{\Omega}\bigtriangledown u_{h} \cdot \bigtriangledown u_{h} dx $ and let $u_{h} = \sum_{i=1}^{n} u_{i} \phi_{i}$.
Solution: $a(u_{h},u_{h}) = ( \bigtriangledown u_{h},\bigtriangledown u_{h} ) = ( \bigtriangledown \sum_{j=1}^{n} u_{j} \phi_{j},\bigtriangledown \sum_{i=1}^{n} u_{i} \phi_{i}) = \sum_{i=1}^{n} \sum_{j=1}^{n} u_{i} u_{j} (\bigtriangledown \phi_{j}, \bigtriangledown \phi_{i}) $
I am not sure how to show this is equal to $u^{T}Au$