Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to solve the following derivative with respect to the scalar parameter [itex]\sigma[/itex]

$$\frac{\partial}{\partial \sigma} \ln|\Sigma|,$$

where [itex]\Sigma = (\sigma^2 \Lambda_K)[/itex] and [itex]\Lambda_K[/itex] is the following symmetric tridiagonal [itex]K \times K[/itex] matrix

$$

\Lambda_{K} =

\left(

\begin{array}{ccccc}

2 & -1 & 0 & \cdots & 0 \\

-1 & 2 & -1 & \cdots & 0 \\

0 & -1 & \ddots & \ddots & \vdots \\

\vdots & \ddots & \ddots & \ddots & -1 \\

0 & 0 & \ldots & -1 & 2 \\

\end{array}\right).

$$

Is there a rule for these case?

Thanks in advance for your time.

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# Derivative of Log Determinant of a Matrix w.r.t a scalar parameter

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