Differential geometry of matrix inversion

Authors

  • Marko Huhtanen

DOI:

https://doi.org/10.7146/math.scand.a-15155

Abstract

Essentially, there exists just the dimension segregating (square) matrix subspaces. In view of algebraic operations, this quantity is not particularly descriptive. For differential geometric information on matrix inversion, the second fundamental form is found for the set of inverses of the invertible elements of a matrix subspace. Several conditions for this form to vanish are given, such as being equivalent to a Jordan subalgebra. Global measures of curvature are introduced in terms of an analogy of the Nash fiber.

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Published

2010-12-01

How to Cite

Huhtanen, M. (2010). Differential geometry of matrix inversion. MATHEMATICA SCANDINAVICA, 107(2), 267–284. https://doi.org/10.7146/math.scand.a-15155

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Articles