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Linear preservers of zeros of matrix polynomials
Beasley, LeRoy B.,Guterman, Alexander E.,Lee, Sang-Gu,Song, Seok-Zun Elsevier 2005 Linear algebra and its applications Vol.401 No.-
<P><B>Abstract</B></P><P>We classify linear operators on matrices with semiring entries that preserve the zeros of multivariable matrix polynomials. These matrix polynomials are defined via the adjoint operator ([<I>X</I>,<I>Y</I>]=<I>XY</I>−<I>YX</I>) as if the matrices were being considered as if over a field. Also we compare the results over fields with the results over semirings.</P>
RANK INEQUALITIES OVER SEMIRINGS
BEASLEY LeRoy B.,GUTERMAN ALEXANDER E. Korean Mathematical Society 2005 대한수학회지 Vol.42 No.2
Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings.
RANK INEQUALITIES OVER SEMIRINGS
LeRoy B. Beasley,Alexander E. Guterman 대한수학회 2005 대한수학회지 Vol.42 No.2
Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings.