The GSVD: Where are the ellipses?, Matrix Trigonometry, and more

@inproceedings{Edelman2019TheGW,
  title={The GSVD: Where are the ellipses?, Matrix Trigonometry, and more},
  author={Alan Edelman and Yuyang Wang},
  year={2019}
}
This paper provides an advanced mathematical theory of the Generalized Singular Value Decomposition (GSVD) and its applications. We explore the geometry of the GSVD which provides a long sought for ellipse picture which includes a horizontal and a vertical multiaxis. We further propose that the GSVD provides natural coordinates for the Grassmann manifold. This paper proves a theorem showing how the finite generalized singular values do or do not relate to the singular values of AB†. We then… CONTINUE READING
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