I am reading something where it seems they have defined a covector/linear functional as a map $F: \mathbb{R}^n \to \mathbb{R}$ where $F$ is a vector
For example, $F(x) = \begin{bmatrix} 1 & 2 \end{bmatrix}x$, $x \in \mathbb{R}^2$. Pick $x = [1, 0]^T$, then $F(x) = 1$. The action of the covector is the standard inner product.
I was super confused because the notation $F(x)$ reminded me of a linear map.
Excuse my ignroance as I have never seen a covector defined this way. Is this a legit covector?