Quadratic Form Representation of Matrix

Suppose that $M=[m_{ij}]$ is a $n\times n$ matrix. The quadratic form $Q_M(h)=h^{T}Mh$ in coordinates:

m_{11} & \dots & m_{1n}\\ \vdots & \dots & \vdots\\ m_{n1} & \dots & m_{nn}\\ \end{array}\right] \left[\begin{array}{cc} h_{1} \\ \vdots \\ h_{n} \\ \end{array}\right] = \sum_{i=1}^{n} \sum_{j=1}^{m} m_{ij}h_{i}h_{j}