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Given that, we want to maximize the posterior probability, for the expression (1) for k, I wan't to know how the expression (2) is obtained: enter image description here

My understanding (may be wrong) is that the expansion should be like this: enter image description here How (3) and (4) are equal?

The article that i'm reading is from https://web.stanford.edu/class/stats202/notes/Classification/LDA.html.

Thanks in advance!

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1 Answer 1

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$x^T\Sigma^{-1}\mu = (x^T\Sigma^{-1}\mu)^T=\mu^T\Sigma^{-1}x$ because it is a scalar and transposing it has no effect. Note that, since $\Sigma$ is symmetric, so as $\Sigma^{-1}$.

Therefore, the last term (4) reduces to $x^T\Sigma^{-1}\mu_k$.

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