To which function does the lambda function refere in this context

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In a tech report from Microsoft there is an equation on page 11 (or actually 16) to calculate the entropy of a d-variate Gaussian density:

$$H(S)={1\over2}log((2\pi e)^d|\Lambda(S)|)$$

I don't know what the $\Lambda(S)$ part of the equation means and what the $\Lambda$ function is. Can someone explain this to me please?

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It's an unusual notation, but presumably it's representing the differential entropy of a multivariate Gaussian random variate S with covariance matrix S.

$\lambda$ in this case represents the determinate.

So your original equation in standard form looks like this:

$$H(S)={1\over2}log((2\pi e)^d|det(S)|)$$

Recommended further reading on the topic: Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing) 99th Edition