I need to show that this matrix is orthogonal. I am not familiar enough with vector properties to simplify the right hand side of the equation. $$ H = I - \frac{2}{xx^T}x^Tx $$ where $I$ is the $n\times n$ identity matrix and the $^{T}$s all refer to transposes. Appreciate any help to get started.
help simplifying vector arithmetic
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linear-algebra