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反特征值理论.
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在应用数学中,反特征值理论(antieigenvalue theory)应用于数值分析、小波、统计学、量子力学、金融以及最优化,由Karl Gustafson于1966至1968年间创立。
一个矩阵或算子
的反特征向量
,是被
作用后旋转角度最大的向量。对应的反特征值
是最大旋转角的余弦。最大旋转角
称为这个算子的角度。就像特征值可以按从小到大的顺序排成谱,反特征值理论把算子
的反特征值按照最大旋转角从小到大的顺序排列。
- Gustafson, Karl (1968), "The angle of an operator and positive operator products", Bulletin of the American Mathematical Society, 74 (3): 488–492, doi:10.1090/S0002-9904-1968-11974-3(页面存档备份,存于互联网档案馆), ISSN 0002-9904, MR 0222668, Zbl 0172.40702
- Gustafson, Karl (2012), Antieigenvalue Analysis, World Scientific, ISBN 978-981-4366-28-1.
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