Decomposition matrix: Difference between revisions

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{{Orphan|date=December 2012}}

In [[mathematics]], and in particular [[modular representation theory]], a '''decomposition matrix''' is a matrix that results from writing the irreducible [[ordinary character]]s in terms of the irreducible [[modular character]]s, where the entries of the two sets of characters are taken to be over all conjugacy classes of elements of order [[coprime]] to the characteristic of the field. All such entries in the matrix are non-negative integers. The decomposition matrix, multiplied by its transpose, forms the [[Cartan matrix]], listing the composition factors of the [[projective modules]].