diff --git a/Gram-matrix-parameterization.md b/Gram-matrix-parameterization.md index f9987e2..e4c4752 100644 --- a/Gram-matrix-parameterization.md +++ b/Gram-matrix-parameterization.md @@ -39,12 +39,7 @@ on $\operatorname{Hom}(\mathbb{R}^n, V)$. Finding a global minimum of the *loss #### The first derivative of the loss function Write the loss function as -\[ -\begin{align*} -f & = \|\Delta\|^2 \\ -& = \operatorname{tr}(\Delta^\top \Delta), -\end{align*} -\] +\[ \begin{align*} f & = \|\Delta\|^2 \\ & = \operatorname{tr}(\Delta^\top \Delta), \end{align*} \] where $\Delta = G - \mathcal{P}(A^\top Q A)$. Differentiate both sides and simplify the result using the transpose-invariance of the trace: \[ \begin{align*}