2019/10/30 by Tianhao Wang, Wang, Tianhao
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #graph theory and CDMA systems #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.1910.13666
Let k be a field and A∈ Mn(k) be an n× n matrix. We denote CMn(k)(A) = \B∈ Mn(k) : BA = AB\ be its centralizers in Mn(k). The dimension of the space of centralizer was already known by Frobenius. This paper will give the explicit k-basis for CMn(k)(A) and also an algorithm (with polynomial complexity respect to multiplication in the field k) to construct the explicit basis. Lastly, the result can be used to solve a weaker version of the Wild Problem.