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An example of linear regression could look like:

$min \sum_{i=0}^{m}||x_i A - y_i||_2^{2}$, where ${x_i, y_i} \in \mathbb{R}^n$ and $A \in \mathbb{R}^{n\times n}$.

I am interested in knowing how do I solve such problem with an of the following extra constraints, $A$ is an orthogonal matrix or $A$ is a rotation matrix.

Notice that a rotation matrix is orthogonal.

kjetil b halvorsen
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aboSamoor
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1 Answers1

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This problem is called the orthogonal Procrustes problem. You can find a closed form solution in terms of the SVD at http://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem.

Stefan Wager
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