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In [[astrodynamics]], the SVD and its variants are used as an option to determine suitable maneuver directions for transfer trajectory design<ref name=muralidharan2023stretching>{{Cite journal|title=Stretching directions in cislunar space: Applications for departures and transfer design|first1=Vivek|last1=Muralidharan|first2=Kathleen|last2=Howell|journal =Astrodynamics | volume = 7 | issue = 2| pages = 153–178 | date = 2023 | doi = 10.1007/s42064-022-0147-z | bibcode = 2023AsDyn...7..153M|s2cid=252637213 }}</ref> and [[orbital station-keeping]].<ref name=Muralidharan2021>{{Cite journal|title=Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits |first1=Vivek|last1=Muralidharan|first2=Kathleen|last2=Howell|journal =[[Advances in Space Research]] | volume = 69 | issue = 1| pages = 620–646 | date = 2022 | doi = 10.1016/j.asr.2021.10.028 | bibcode = 2022AdSpR..69..620M|s2cid=239490016 }}</ref>
The SVD can be used to measure the similarity between real-valued matrices<ref name=albers2025>{{Cite journal|title=Assessing the Similarity of Real Matrices with Arbitrary Shape|first1=Jasper|last1=Albers|first2=Anno|last2=Kurth|first3=Robin|last3=Gutzen|first4=Aitor|last4=Morales-Gregorio|first5=Michael|last5=Denker|first6=Sonja|last6=Gruen|first7=Sacha|last7=van Albada|first8=Markus|last8=Diesmann|journal=PRX Life| issue = 3| pages = 023005 | date = 2025 | doi = 10.1103/PRXLife.3.023005 }}</ref>. By measuring the angles between the singular vectors, the inherent two-dimensional structure of matrices is accounted for. This method was shown to outperform [[cosine similarity]] and [[Frobenius norm]] in most cases, including brain activity measurements form [[neuroscience]].
== Proof of existence ==
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