There’s no real reason to think of column vectors as points in space rather than the other way around when you’re doing linear algebra. It’s just a convention.

There’s no real reason to think of column vectors as points in space rather than the other way around when you’re doing linear algebra. It’s just a convention. If you wanted, you could think of a row vector as a point in space and transpose everything. In that case, your dual space of linear functionals would consist of column vectors rather than row vectors.