I'm new to this notation: $$ F=(F_1,F_2, \dots, F_m) $$ where $F:\mathbb{R}^n \rightarrow \mathbb{R}^m$.
No boldface or variables. Is this a abbreviation for a vector field?
I mean, is the explicit form actually a vector $\mathbf{x}=(x_1,x_2,\dots, x_n)$ in $\mathbb{R}^n$ and $$ F(\mathbf{x})=(F_1(\mathbf{x}), F_2(\mathbf{x}), \dots, F_m(\mathbf{x})) \iff $$ $$ F(x_1,x_2,\dots, x_n)=(F_1(x_1,x_2,\dots, x_n), F_2(x_1,x_2,\dots, x_n), \dots, F_m(x_1,x_2,\dots, x_n)) $$ in $\mathbb{R}^m$? Is this a correct interpretation of the notation?