Abstract
We present a new approach to the problem of recognizing an Euclidean distance matrix, based on Conformal Geometric Algebra. Such matrices are symmetric and hollow with non negative entries that are equal to the squared distances among the set of points. In addition to find these points, the method presented here also provides the minimal dimension of the related space. A comparison with a linear algebra approach is also provided.
Supported by organization CAPES, FAPESP, CNPq.
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Notes
- 1.
An i-sphere is the intersection of a sphere with an affine subspace of dimension i.
- 2.
We recall that the reverse of a blade is another blade with the reverted order of the factors in the exterior product.
- 3.
The center of a point pair is regarded as the midpoint of the segment connecting the two points.
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Acknowledgements
We would like to thank the Brazilian research agencies FAPESP, CAPES and CNPq, and the reviewers for the useful comments.
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Riter, V., Alves, R., Lavor, C. (2024). Geometric Algebra and Distance Matrices. In: Silva, D.W., Hitzer, E., Hildenbrand, D. (eds) Advanced Computational Applications of Geometric Algebra. ICACGA 2022. Lecture Notes in Computer Science, vol 13771. Springer, Cham. https://doi.org/10.1007/978-3-031-34031-4_8
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