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About: Manin matrix     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatMatricesyago:Abstraction100002137yago:Arrangement107938773yago:Array107939382yago:Group100031264yago:Matrix108267640 New Facet based on Instances of this Class

In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute. In particular there is natural definition of the determinant for them and most linear algebra theorems like Cramer's rule, Cayley–Hamilton theorem, etc. hold true for them. Any matrix with commuting elements is a Manin matrix. These matrices have applications in representation theory in particular to Capelli's identity, Yangian and quantum integrable systems.