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my linear algebra is a bit rusty and I'm having trouble performing the following operation

$(\mu_1-\mu_0)^{T}\Sigma^{-1}(\mu_1-\mu0)$

Both $\mu_1$ and $\mu_0$ are two-dimensional vectors. $\Sigma$ is a 2x2 matrix.

I assume this means we take the transpose of the vector difference, multiply it by the inverse of the matrix and further multiply by the vector difference.

If I am not entirely wrong this means we have to do the dot product between

$\begin{pmatrix}a \\ b\end{pmatrix} \begin{pmatrix}c & d \\ e & f \end{pmatrix} \begin{pmatrix}g & h \end{pmatrix}$

As far as I can remember the number of columns in the left side matrix must match the number of rows in the right side matrix which is not the case here. The entire formula is here in case it helps put things into context. Any help would be appreciated.

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  • $\begingroup$ Welcome to Mathematics Stack Exchange. Try $ \begin{pmatrix}a& b \end{pmatrix}\begin{pmatrix}c & d \\ e & f \end{pmatrix}\begin{pmatrix}g \\ h\end{pmatrix} $ $\endgroup$ Nov 20 '19 at 18:02
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This should be done on a column vector. The transposed vector on the left will then be a row vector, with the column vector on the right, thus making the product well defined.

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