I am trying to generate some data. Can someone explain what "100 points in $R^{10}$" means? From my small understanding, this should be a matrix $10\times 100$. Is this correct?
100 points in $R^{10}$
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linear-algebra
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3Both users give good answers below. I'll add that if you're using code written by someone else, check what format they want the data in. In particular, check that the data is stored "row-wise" or "column-wise". Mathematically, it doesn't really matter, but it will matter in the implementation. – 2017-01-12
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A point in $\Bbb R^{k}$ is a vector with $k$ components. If you want one point in $\Bbb R^{10}$ then you want a vector with $10$ components.
Given that you want $100$ points, you need $100$ vectors. One way of representing them would be in a $100\times10$ matrix, where each row would be one of your points, or on a $10\times100$ matrix, where each column would be one of your points.
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$\mathbb{R}^{10}$ is the set of all $10$-tuples with real entries (i.e: the entries are real numbers in $\mathbb{R}$). For example,
$$\begin{pmatrix}2\\ 4.312\\ 5\\ 6.7\\ 2\\ 0.6\\ 4\\ 2\\ 7.8\\ 9.3\end{pmatrix} \in \mathbb{R}^{10}.$$
To answer your second question: yes, $100$ points in $\mathbb{R}^{10}$ can be represented by a $10 \times 100$ matrix if the points are represented as columns (as in the above example). If each point is represented by a row, then you would use a $100 \times 10$ matrix.