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低秩SVD在从时空数据中检测热点方面表现出色，已应用于疾病爆发检测<ref>{{citation | last1=Fanaee Tork | first1=Hadi | last2=Gama | first2=João | date=September 2014 | title="Eigenspace method for spatiotemporal hotspot detection" | journal=Expert Systems | volume=32 | issue=3 | pages=454–464 | doi=10.1111/exsy.12088 | arxiv=1406.3506 | bibcode=2014arXiv1406.3506F|s2cid=15476557}}</ref>。研究人员还将SVD和高阶SVD结合起来，用于疾病监测中从复杂数据流(具有空间和时间维度的多变量数据)进行实时事件检测<ref>{{citation | last1=Fanaee Tork | first1=Hadi | last2=Gama | first2=João | date=May 2015 | title="EigenEvent: An Algorithm for Event Detection from Complex Data Streams in Syndromic Surveillance" | journal=Intelligent Data Analysis | volume=19 | issue=3 | pages=597–616 | doi=10.3233/IDA-150734 | arxiv=1406.3496|s2cid=17966555}}</ref>。
低秩SVD在从时空数据中检测热点方面表现出色，已应用于疾病爆发检测<ref>{{citation | last1=Fanaee Tork | first1=Hadi | last2=Gama | first2=João | date=September 2014 | title="Eigenspace method for spatiotemporal hotspot detection" | journal=Expert Systems | volume=32 | issue=3 | pages=454–464 | doi=10.1111/exsy.12088 | arxiv=1406.3506 | bibcode=2014arXiv1406.3506F|s2cid=15476557}}</ref>。研究人员还将SVD和高阶SVD结合起来，用于疾病监测中从复杂数据流(具有空间和时间维度的多变量数据)进行实时事件检测<ref>{{citation | last1=Fanaee Tork | first1=Hadi | last2=Gama | first2=João | date=May 2015 | title="EigenEvent: An Algorithm for Event Detection from Complex Data Streams in Syndromic Surveillance" | journal=Intelligent Data Analysis | volume=19 | issue=3 | pages=597–616 | doi=10.3233/IDA-150734 | arxiv=1406.3496|s2cid=17966555}}</ref>。
在天体动力学（astrodynamics）领域，科学家们运用SVD及其变体来确定转移轨道设计<ref>{{citation | last1=Muralidharan | first1=Vivek | last2=Howell | first2=Kathleen | date=2023 | title="Stretching directions in cislunar space: Applications for departures and transfer design" | journal=Astrodynamics | volume=7 | issue=2 | pages=153–178 | doi=10.1007/s42064-022-0147-z |s2cid = 252637213|bibcode=2023AsDyn...7..153M}}</ref>和轨道站保持的合适机动方向<ref>{{citation | last1=Muralidharan | first1=Vivek | last2=Howell | first2=Kathleen | date=2022 | title="Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits" | journal=Advances in Space Research | volume=69 | issue=1 | pages=620–646 | doi=10.1016/j.asr.2021.10.028 | bibcode=2022AdSpR..69..620M|s2cid=239490016}}</ref>。
在天体动力学（astrodynamics）领域，科学家们运用SVD及其变体来确定转移轨道设计<ref>{{citation | last1=Muralidharan | first1=Vivek | last2=Howell | first2=Kathleen | date=2023 | title="Stretching directions in cislunar space: Applications for departures and transfer design" | journal=Astrodynamics | volume=7 | issue=2 | pages=153–178 | doi=10.1007/s42064-022-0147-z |bibcode=2023AsDyn...7..153M}}</ref>和轨道站保持的合适机动方向<ref>{{citation | last1=Muralidharan | first1=Vivek | last2=Howell | first2=Kathleen | date=2022 | title="Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits" | journal=Advances in Space Research | volume=69 | issue=1 | pages=620–646 | doi=10.1016/j.asr.2021.10.028 | bibcode=2022AdSpR..69..620M|s2cid=239490016}}</ref>。
==存在性证明==
==存在性证明==