Search results
Results from the WOW.Com Content Network
The Jordan form is used to find a normal form of matrices up to conjugacy such that normal matrices make up an algebraic variety of a low fixed degree in the ambient matrix space. Sets of representatives of matrix conjugacy classes for Jordan normal form or rational canonical forms in general do not constitute linear or affine subspaces in the ...
Indeed, determining the Jordan normal form is generally a computationally challenging task. From the vector space point of view, the Jordan normal form is equivalent to finding an orthogonal decomposition (that is, via direct sums of eigenspaces represented by Jordan blocks) of the domain which the associated generalized eigenvectors make a ...
A matrix normal form or matrix canonical form describes the transformation of a matrix to another with special properties. Pages in category "Matrix normal forms" The following 10 pages are in this category, out of 10 total.
The Jordan normal form and the Jordan–Chevalley decomposition. Applicable to: square matrix A; Comment: the Jordan normal form generalizes the eigendecomposition to cases where there are repeated eigenvalues and cannot be diagonalized, the Jordan–Chevalley decomposition does this without choosing a basis.
Over an algebraically closed field of positive characteristic, the representation theory of a finite cyclic group is fully explained by the theory of the Jordan normal form. Non-diagonal Jordan forms occur when the characteristic divides the order of the group.
The decomposition has a short description when the Jordan normal form of the operator is given, but it exists under weaker hypotheses than are needed for the existence of a Jordan normal form. Hence the Jordan–Chevalley decomposition can be seen as a generalisation of the Jordan normal form, which is also reflected in several proofs of it.
Hesse normal form; Normal form in music; Jordan normal form; in formal language theory: Chomsky normal form; Greibach normal form; Kuroda normal form; Normal form (abstract rewriting), an element of a rewrite system which cannot be further rewritten; in logic: Normal form (natural deduction) Algebraic normal form; Canonical normal form; Clausal ...
The Drazin inverse is then the operation that maps invertible Jordan blocks to their inverses, and nilpotent Jordan blocks to zero. More generally, we may define the Drazin inverse over any perfect field , by using the Jordan-Chevalley decomposition A = A s + A n {\displaystyle A=A_{s}+A_{n}} where A s {\displaystyle A_{s}} is semisimple and A ...