Components of Algebraic Sets of Commuting and Nearly Commuting Matrices.
[摘要] In this thesis we study algebraic sets of tuples whose entries are mutually com-muting matrices possibly satisfying some additional condition, such as nilpotence, orwhich satisfy some weakening of the condition of commutativity. For example, westudy pairs of matrices whose commutator is nilpotent, and also those pairs whosecommutator is a diagonal matrix. In particular, we study several instances in whichsuch algebraic sets are complete intersections, and also investigate the behavior ofthe components of these algebraic sets. In some instances, it is remarkably dicultto prove irreducibility, or to determine explicitly how many components there are.
[发布日期] [发布机构] University of Michigan
[效力级别] Mathematics [学科分类]
[关键词] Nearly Commuting Matrices;Mathematics;Science;Mathematics [时效性]