2010
DOI: 10.7146/math.scand.a-15155
|View full text |Cite
|
Sign up to set email alerts
|

Differential geometry of matrix inversion

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… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
6
0

Year Published

2010
2010
2019
2019

Publication Types

Select...
5

Relationship

3
2

Authors

Journals

citations
Cited by 5 publications
(6 citation statements)
references
References 20 publications
0
6
0
Order By: Relevance
“…Generically a matrix subspace is nonsingular; see [18] for a qualitative treatment of nonsingular matrix subspaces in view of matrix inversion. With dim V = 1 we are dealing with the standard notion of nonsingularity of a matrix.…”
Section: Matrix Intersection Problems For Conditioning Of Matrix Subsmentioning
confidence: 99%
“…Generically a matrix subspace is nonsingular; see [18] for a qualitative treatment of nonsingular matrix subspaces in view of matrix inversion. With dim V = 1 we are dealing with the standard notion of nonsingularity of a matrix.…”
Section: Matrix Intersection Problems For Conditioning Of Matrix Subsmentioning
confidence: 99%
“…We experiment with three matrices A by solving the preconditioned linear system (5.1) with GMRES (20). The matrices sherman1 and orsreg1 arise in oil reservoir simulation and jpwh991 in circuit simulation.…”
Section: Example 51mentioning
confidence: 99%
“…Then n = 3564 with nz(A) = 22316 and a condition number estimate κ(A) = 1E + 2. In [14] it was reported that when SPAI is used to precondition the problem, GMRES (20) does not converge within 1000 iterations.…”
Section: Example 51mentioning
confidence: 99%
See 2 more Smart Citations