What is the mathematical meaning of $xx^T$ Assume x is a n by 1 column vector, then , it is easily known that $x^Tx$ is the sum of squares. When calculate $xx^T$, it will give you a n by n matrix. I am wondering what is the mathematical meaning of such results.

If $x$ has length 1, then $xx^T$ is the orthogonal projection on the subspace of $\mathbb{R}^n$ (endowed with the canonical scalar product) generated by $x$. 
