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This should be a comment. I think this question is not apt here. You should consider posting questions like these at math.stackexchangemath.stackexchange.

Given $U$ and if it is full rank, we can choose $$V = -2 \left(UU^T \right)^{-1}U$$ and the matrix $$W = I - 2 U^T \left(UU^T \right)^{-1}U$$ is an orthonormal matrix. A special case of this is provided by Jeff.

This should be a comment. I think this question is not apt here. You should consider posting questions like these at math.stackexchange.

Given $U$ and if it is full rank, we can choose $$V = -2 \left(UU^T \right)^{-1}U$$ and the matrix $$W = I - 2 U^T \left(UU^T \right)^{-1}U$$ is an orthonormal matrix. A special case of this is provided by Jeff.

This should be a comment. I think this question is not apt here. You should consider posting questions like these at math.stackexchange.

Given $U$ and if it is full rank, we can choose $$V = -2 \left(UU^T \right)^{-1}U$$ and the matrix $$W = I - 2 U^T \left(UU^T \right)^{-1}U$$ is an orthonormal matrix. A special case of this is provided by Jeff.

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user11000
user11000

This should be a comment. I think this question is not apt here. You should consider posting questions like these at math.stackexchange.

Given $U$ and if it is full rank, we can choose $$V = -2 \left(UU^T \right)^{-1}U$$ and the matrix $$W = I - 2 U^T \left(UU^T \right)^{-1}U$$ is an orthonormal matrix. A special case of this is provided by Jeff.