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# Kabsch Algorithm
## Introduction

The Kabsch algorithm, named after Wolfgang Kabsch, computes the optimal rotation matrix for two sets of points so that the [RMSD](https://en.wikipedia.org/wiki/Root-mean-square_deviation_of_atomic_positions) (Root mean squared deviation) is minimal. In Bioinformatics this applies to superimposing the C<sub>&alpha</sub> atomic coordinates of two protein structures.
The Kabsch algorithm, named after Wolfgang Kabsch, computes the optimal rotation matrix for two sets of points so that the [RMSD](https://en.wikipedia.org/wiki/Root-mean-square_deviation_of_atomic_positions) (Root mean squared deviation) is minimal. In Bioinformatics this applies to superimposing the C<sub>&alpha;</sub> atomic coordinates of two protein structures.

To illustrate this the following excerpt of the [PDB](https://www.wwpdb.org/documentation/file-format) file of [human deoxyhaemoglobin](http://www.rcsb.org/pdb/explore/explore.do?structureId=2HHB) shows part of one of the alpha chains of the structure. The C<sub>&alpha</sub> atomic coordinates shown can be used to construct a reference matrix which together with another matrix of coordinates (constructed the same way) could serve as the input of the algorithm.
To illustrate this the following excerpt of the [PDB](https://www.wwpdb.org/documentation/file-format) file of [human deoxyhaemoglobin](http://www.rcsb.org/pdb/explore/explore.do?structureId=2HHB) shows part of one of the alpha chains of the structure. The C<sub>&alpha;</sub> atomic coordinates shown can be used to construct a reference matrix which together with another matrix of coordinates (constructed the same way) could serve as the input of the algorithm.

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