# Questions tagged [procrustes-problem]

The Orthogonal Procrustes Problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices, $A$ and $B$, and is asked to find an orthogonal matrix $R$ that most closely maps $A$ to $B$.

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### I want to solve the orthogonal procrustses problem, but I am confused by the deformed form.

I'm studying about orthogonal Procrustses problem. Now, I wonder if there is a way to solve the orthogonal procrustses problem when the orthogonal matrix $Q$ is located in two or more terms. Also, the ...
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### Solving a variant of an orthogonal Procrustes problem

While reading the following paper on an optimization problem, there was a variant of an orthogonal Procrustes problem, where the solution is an element of the Stiefel manifold. The authors provided a ...
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### Find $Q$ in $R_2 = Q^TR_1Q$ where all matrices $R_1, R_2, Q$ are 3x3 rotations

Can we obtain $Q$ in $$R_2 = Q^TR_1Q$$ where $R_1, R_2, Q$ are all 3x3 rotation matrices, $R_1 \ne R2$, and $\operatorname{trace}(R_1)=\operatorname{trace}(R_2)$? I have a problem where $R_1$ and $R_2$...
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### Projection onto the Stiefel manifold and the orthogonal Procrustes problem

Let $m$ and $n$ be positive integers such that $m \ge n$, the case with $m >n$ being particularly interesting to us. The Stiefel manifold is \mathbb{S}^{m, n} = \{X \in \mathbb{R}^{...
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### Matrix derivative in images matching problem

Problem Suppose zero-centered matrices $\mathbf{X}$ and $\mathbf{Y}$ of shape $\mathbb{R}^{n\times 2}$. Each row of $\mathbf{X}$ and $\mathbf{Y}$ represents a point on 2-D plane. Therefore, they each ...
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