What does the $t$ in $(x,y,z)^t$ mean?
Just a question on notation. I have seen a plane defined this way:
$$S = \{(x,y,z)^t \in \mathbb{R}^3 \ / \ 2x-3y+z = 0\}$$
See the $t$ superscript on $(x,y,z)$? Well, I am not quite sure what is it. I know this is pretty basic, because I've seen it several times in the past, but always disregarded it (and my exercises still worked out just fine).
What is it supposed to represent?
If I had to make a wild guess, I would say that $(x,y,z)$ is one row of a matrix - and $(x,y,z)^t$ is its traspose (therefore it is a column of a matrix). But, that doesn't make much sense to me, and don't see how is this relevant.
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$\begingroup$Yes, it is the transpose. Usually, one works with column vectors, that is, if $\Bbb R^n$ is to be related to matrix algebra, it is commonly identified with $\Bbb R^{n\times 1}$.
However, for your task it is irrelevant, it works as well in tuple vector space without identifying row or column.
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