How to add vector with itself tranposed? So I'm solving basic linear algebra questions as part of review.
$$v=\begin{bmatrix} 1 & 2 & 3 \\ \end{bmatrix}$$
When I do the operation $v+v^T$ according to matlab, numpy and wolfram alpha
spits out
$$v+v^T=\begin{bmatrix} 2 & 3 & 4\\  3 & 4 & 5\\ 4 & 5 & 6\\ \end{bmatrix}$$
Originally I thought it would be like 
$$ v + v^T = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \\ 1 & 2 & 3\\ \end{bmatrix} + \begin{bmatrix} 1 & 1 & 1 \\ 2 & 2 & 2 \\ 3 & 3 & 3\\ \end{bmatrix}=\begin{bmatrix} 2 & 3 & 4\\  3 & 4 & 5\\ 4 & 5 & 6\\ \end{bmatrix}$$
Can someone explain to be how this makes any sense?


Can someone explain to be how this makes any sense?

It doesn't make any sense.
If you're talking about tansposition, then you're implicitly viewing your vectors as matrices with one of the dimensions being $1$.
Then your $v$ is a $1\times 3$ matrix and $v^T$ is a $3\times 1$ matrix.
Addition of matrices that don't have the same dimension is not defined.
