I have a set of n-dimensional vectors, lets say, v1, v2, v3, ... vm
<vi, vj> means the dot product of vi and vj.
It is known that <vi, vj> >= 0 forall i, j .... i.e. the angle between any
two of them is less equal to 90 degrees, which basically means that all of
them can be occupied in a single quadrant in the n-dimensional space.
Because in any quadrant, the maximum angle between two vectors both lying
inside the quadrant is 90 degrees.
Can you come up with a orthonormal transformation U, such that Uvi >= 0 ...
i.e. an orthonormal transformation (rotation basically, i want the rotation
matrix U), such that all those vectors come in the positive quadrant.
There will always exist such a matrix U because all the angles are less than
90degrees, can you get a way to find one of them.
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Indian Institute of Technology Kanpur
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