In mathematics, the quasideterminant is a replacement for the determinant for matrices with noncommutative entries. Example 2 × 2 quasideterminants are as follows: In general, there are n2 quasideterminants defined for an n × n matrix (one for each position in the matrix), but the presence of the inverted terms above should give the reader pause: they are not always defined, and even when they are defined, they do not reduce to determinants when the entries commute. Rather, where means delete the ith row and jth column from A. The examples above were introduced between 1926 and 1928 by Richardson and Heyting, but they were marginalized at the time because they were not polynomials in the entries of . These examples were rediscovered and given new life in 1991 by Israel Gelfand and Vladimir Retakh. There, they develop quasideterminantal versions of many familiar determinantal properties. For example, if is built from by rescaling its -th row (on the left) by , then . Similarly, if is built from by adding a (left) multiple of the -th row to another row, then . They even develop a quasideterminantal version of Cramer's rule. (Wikipedia).
Numerical mathematics of quasicrystals – Pingwen Zhang – ICM2018
Numerical Analysis and Scientific Computing Invited Lecture 15.8 Numerical mathematics of quasicrystals Pingwen Zhang Abstract: Quasicrystals are one kind of fascinating aperiodic structures, and give a strong impact on material science, solid state chemistry, condensed matter physics an
From playlist Numerical Analysis and Scientific Computing
Jean Michel : Quasisemisimple classes
Abstract: This is a report on joint work with François Digne. Quasisemisimple elements are a generalisation of semisimple elements to disconnected reductive groups (or equivalently, to algebraic automorphisms of reductive groups). In the setting of reductive groups over an algebraically c
From playlist Lie Theory and Generalizations
Ex: Determinant of a 2x2 Matrix
This video provides two examples of calculating a 2x2 determinant. One example contains fractions. Site: http://mathispower4u.com
From playlist The Determinant of a Matrix
Equaivalent statements about the determinant. Evaluating elementary matrices.
From playlist Linear Algebra
Constructing group actions on quasi-trees – Koji Fujiwara – ICM2018
Topology Invited Lecture 6.12 Constructing group actions on quasi-trees Koji Fujiwara Abstract: A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary hype
From playlist Topology
In this video, I define the notion of adjugate matrix and use it to calculate A-1 using determinants. This is again beautiful in theory, but inefficient in examples. Adjugate matrix example: https://youtu.be/OFykHi0idnQ Check out my Determinants Playlist: https://www.youtube.com/playlist
From playlist Determinants
(3.2.3) The Determinant of Square Matrices and Properties
This video defines the determinant of a matrix and explains what a determinant means in terms of mapping and area. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Schemes 27: Quasicoherent sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We show how to turn a module over a ring into a sheaf of modules over its spectrum. A quasicoherent sheaf of modules of one which looks locally like one constr
From playlist Algebraic geometry II: Schemes
Generalized eigenvectors. Generalized eigenspaces. Generalized eigenvectors corresponding to distinct eigenvalues are linearly independent.
From playlist Linear Algebra Done Right
Watch more videos on http://www.brightstorm.com/math
From playlist Precalculus