I'm reading the definition of left-multiplication transformation, and it says ["]*for each column vector $x\in\mathsf{F}^n$*[."], but my original understanding is that each element of $\mathsf{F}^n$ is a tuple. I know in this definition it should be a column vector, or it will be a problem of how to place a tuple into column vector, i.e. vertically from top to bottom or bottom to top, to multiply it with a matrix. I'm confused about what's the actual meaning of $\mathsf{F}^n$. So is that

$$\textrm{["]Read a tuple left to right then it means the same thing of reading a column vector top-down[."]},$$

a convention?

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[![Definition of left-multiplication transformation](https://i.stack.imgur.com/Qw6gz.png)](https://i.stack.imgur.com/Qw6gz.png)

And why I thought it could be a tuple can be traced back to another page of the same book

[![enter image description here](https://i.stack.imgur.com/CdIuW.png)](https://i.stack.imgur.com/CdIuW.png)