High Quality Content by WIKIPEDIA articles!In mathematics, absolutely irreducible is a term applied to linear representations or algebraic varieties over a field. It means that the object in question remains irreducible, even after any finite extension of the field of coefficients. In both cases, being absolutely irreducible is the same as being irreducible over the algebraic closure of the ground field.Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication.

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