[Math] How does v * vT equal a matrix

linear algebramatrices

I don't understand how a vector * vector.T results in a matrix? Shouldn't the result be a single product?

For instance

(2/root(6), 1/root(6), 1/root(6))

multiplied with its transposed form.

Maybe I am confused as to how to multiply a vector with a transposed vector.

Best Answer

When you multiply a $3\times1$ vector by a $1\times3$ vector the result is $(3\times1)\cdot(1\times3)=3\times3$.

On the other hand, when you multiply a $1\times3$ vector by a $3\times1$ vector, you get $(1\times3)\cdot(3\times1)=1\times1$ (this is the inner product, aka the dot product)

The image in this answer is the easiest way to visualize this, imo.

Related Question