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## Homework Statement

I need help with expanding:

[itex](\bf{x-\mu_{i}})^{t}\Sigma^{-1}(\bf{x-\mu_{i}})[/itex]

[itex]\bf{x,\mu_{i}}[/itex] are column vectors.

[itex]\Sigma[/itex] is a square matrix.

Thank you.

## Homework Equations

Can:

[itex]

\bf{x}^t\Sigma^{-1}\bf{\mu_{i}}

[/itex]

be written as?

[itex]

\bf{\mu_{i}}^t\Sigma^{-1}\bf{x}

[/itex]

I've tried to compute this numerically and the answer is no.

## The Attempt at a Solution

[itex]

(\bf{x-\mu_{i}})^{t}\Sigma^{-1}(\bf{x-\mu_{i}})

=

\bf{x}^t\Sigma^{-1}\bf{x}+

\bf{\mu_{i}}^t\Sigma^{-1}\bf{\mu_{i}}-

\bf{x}^t\Sigma^{-1}\bf{\mu_{i}}-

\bf{\mu_{i}}^t\Sigma^{-1}\bf{x}

[/itex]