I can generate a random vector with
a = torch.rand(10)
>>> tensor([0.6432, 0.7512, 0.8835, 0.4268, 0.7681, 0.4709, 0.2722, 0.0510, 0.8463,
0.9003])
However, how can I generate N more vectors (e.g. N=5: b,c,d,e,f) that will be linearly independent of the other vectors (i.e a is independent of any of b,c,d,e,f, b is independent of any of a,c,d,e,f, etc.)?
I can think of two ways to achieve this. However, there are some restrictions to each of them.
For an n-dimensional space, the first way is to create n random vectors and check for linear independence using determinants. Check out here for more information about the process.
The second way is to generate vectors one by one. Create a random vector, then using this solution, create a new independent vector, then create the third one, and so on.