TL;DR
This paper determines the dimensions and codimensions of sets of matrices with specified eigenvalue, Jordan form, and singular value multiplicities, providing a comprehensive understanding of their structural constraints.
Contribution
It calculates the dimensions and codimensions of matrix sets with prescribed eigenvalue, Jordan form, and singular value multiplicities, extending previous results in matrix theory.
Findings
Dimensions of sets with specified eigenvalue multiplicities
Dimensions of sets with given Jordan form
Dimensions of sets with specified singular value multiplicities
Abstract
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each corresponding codimension is the number of conditions which a matrix of the given type must satisfy in order to have the specified multiplicities.
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