Polytopes of majorization and g-majorization
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2009
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Maltepe Üniversitesi
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Abstract
Let Mn and Mn,m be the vector spaces of all n × n and n × m matrices respectively with entries in the field of real numbers. A nonnegative (or not necessarily nonnegative) matrix R ? Mm is called row stochastic (or g-row stochastic) if Re = e where e = (1, ..., 1)t ? Mn,1 . For matrices A, B ? Mn,m , it is said that A is majorized (or g-majorized) by B from right if there exists a row stochastic (or g-row stochastic) matrix R ? Mm such that A = BR. The polytopes of majorization and g-majorization for given matrices A, B ? Mn,m denoted by P (A ? B) and P (A ?g B) respectively and defined as the following convex sets: P (A ? B) := {R : R is a row stochastic matrix and A = BR}, P (A ?g B) := {R : and R is a g-row stochastic matrix and A = BR}. In this paper, we investigate some properties of polytopes of majorization and g-majorization for some special types of matrices A, B ? Mn,m . Also we will find the dimension of the linear vector spaces generated by P (A ? B) or P (A ?g B)
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International Conference of Mathematical Sciences
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Armandnejad, A. (2009). Polytopes of majorization and g-majorization. Maltepe Üniversitesi. s. 81.
