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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 ...
Jordan normal form is a canonical form for matrix similarity. The row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix . In computer science, and more specifically in computer algebra , when representing mathematical objects in a computer, there are usually many different ...
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 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.
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 De Morgan dual is the canonical conjunctive normal form , maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.