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Set of All MXN Rectangular Real Matrices of Rank-R Is Connected by Analytic Regular Arcs, The

Evard, J. C.
; 
Jafari, Farhad
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It is well known that the set of all square invertible real matrices has two connected components. The set of all m x n rectangular real matrices of rank r has only one connected component when m ≠ n or r < m = n. We show that all these connected components are connected by analytic regular arcs. We apply this result to establish the existence of p-times differentiable bases of the kernel and the image of a rectangular real matrix function of several real variables.
Date
1994-02-01
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University of Wyoming. Libraries
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Mathematics
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https://wyoscholar.uwyo.edu/handle/internal/1695
 https://doi.org/10.15786/wyoscholar/9684
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Faculty Publications | Mathematics and Statistics
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