If $\mathbf{x}$ is a vector and $Q$ a symmetric Matrix; Does $Q\mathbf{x} = \mathbf{x}^T Q$ ?
EDIT :
I have this: $\frac{1}{2}\left(Q\mathbf{x} + \mathbf{x}^TQ\right) + \mathbf{c},$ where $\mathbf{c}$ is also a vector, and I want to obtain $Q\mathbf{x}+\mathbf{c}$.
I thought that was the answer to my question, but it doesn't seem to be. Do you see a way to obtain this?
EDIT : Well Then I believe I made an error prior that, I can explain what I have done before to see if it's the source of the error.
I am trying to find the gradient of the function $\frac{1}{2}\left(\mathbf{x}^TQ\mathbf{x}\right) + \mathbf{c}\mathbf{x}$
that's how I got the first answer by finding the gradient.