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.

A similar formula can be written for each distinct eigenvalue of a matrix A. The collection of formulas are called Jordan chain relations. A given eigenvalue may appear multiple times in …

Such a matrix is called a Jordan block of size m with eigenvalue λ1. Its characteristic polynomial is (λ1 − λ)m, so the only eigenvalue is λ1, and the eigenspace corresponding to this eigenvalue …

A Jordan block with eigenvalue λ is a square matrix whose entries are equal to λ on the diagonal, equal to 1 right below the diagonal and equal to 0 elsewhere.

Jul 26, 2023 · Thus, for example, two matrices (or two operators) are similar if and only if they have the same Jordan canonical form. We omit the proof of uniqueness; it is best presented …

In a Jordan matrix, the eigenvalues are on the diagonal and there may be ones above the diagonal; the rest of the entries are zero. The number of blocks is the number of eigenvectors …

Theorem 3.12 tells us that T has a Jordan canonical form, and that is is moreover one of the above matrices A, B, C. Our goal is to develop a method whereby the pattern of cycle-lengths …

A matrix is said to be in Jordan form if 1) its diagonal entries are equal to its eigenvalues; 2) its supradiagonal entries are either zeros or ones; 3) all its other entries are zeros.

Tool to calculate the Jordan Normal Form of a Matrix (by Jordan reduction of a square matrix) to get, by decomposition, 2 matrices S and J such that M = S . J .

In linear algebra, a Jordan canonical form (JCF) or a Jordan normal form is an upper triangular matrix of a unique format called a Jordan matrix which illustrates a linear operator on a finite …