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.
Add to solve later Tagged: transpose of a vector
Add to solve later The Length of a Vector is Zero if and only if the Vector is the Zero Vector
Problem 639
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 $\mathbf{0}$.
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