Quasideterminants
By I. Gelfand, S. Gelfand, V. Retakh, R. Wilson. 2002
236 citations recorded by the source corpus.
The determinant is a main organizing tool in commutative linear algebra. In this review we present a theory of the quasideterminants defined for matrices over a division algebra. We believe that the notion of quasideterminants should be one of main organizing tools in noncommutative algebra giving them the same role determinants play in commutative algebra.
View Paper: https://www.semanticscholar.org/paper/0050738b446fcccab88dda5029e0afb9bc135051
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- Dmitry S. Kaliuzhnyi-Verbovetskyi
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Citations in the corpus
- Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables (2001, background): “First it was introduced in [20], see also [21], [22], [24] and references therein for further developments and applications.”
- Foundations of Free Noncommutative Function Theory (2012, background): “Quasideterminants [44, 45, 42] and nc symmetric functions [43] are important examples of nc rational functions, whereas formal Baker–Campbell–Hausdorff series [36] are an important example of nc formal power series.”
- The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for \hat gl(m|n) (2009, methodology): “Explicit formulas for the entries of the matrices D(u), E(u) and F (u) can be given in terms of quasideterminants; see [14].”