I would like to decompose the matrix,
\begin{equation\*}
 \mathbf{C}=\sigma\_w^2
 \begin{bmatrix}
 f\_2^2&f\_1f\_2&0\\[10pt]
 f\_1f\_2&f\_1^2+f\_2^2&f\_1f\_2\\[10pt]
 0&f\_1f\_2&f\_1^2
 \end{bmatrix}
 \end{equation\*}
into,
$$\mathbf{C}=\mathbf{f}.\mathbf{f}^T\sigma\_w^2$$

Is there a technique to solve for $\mathbf{f}$?