Prove that $\mathbf{v} \mathbf{v}^\trans$ is a Symmetric Matrix for any Vector $\mathbf{v}$
Problem 640
Let $\mathbf{v}$ be an $n \times 1$ column vector.
Prove that $\mathbf{v} \mathbf{v}^\trans$ is a symmetric matrix.

Let $\mathbf{v}$ be an $n \times 1$ column vector.
Prove that $\mathbf{v} \mathbf{v}^\trans$ is a symmetric matrix.
Let $\mathbf{v}$ be an $n \times 1$ column vector.
Prove that $\mathbf{v}^\trans \mathbf{v} = 0$ if and only if $\mathbf{v}$ is the zero vector $\mathbf{0}$.