Abstract
Two square matrices A and B over a ring R are semisimilar, written A ⋍ B , if YAX = B and XBY = A for some (possibly rectangular) matrices X , Y over R . We show that if A and B have the same dimension, and if the ring is a division ring D , then A ⋍ B if and only if A 2 is similar to B 2 and rank( A k )=rank( B k ), k =1,2,…
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