algebra, a Jordan normal form, also known as a Jordan canonical form, is an upper triangular matrix of a particular form called a Jordan matrix representing...

form Normal form in music Jordan normal form in formal language theory: Chomsky normal form Greibach normal form Kuroda normal form Normal form (abstract...

algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained...

defined, a canonical form consists in the choice of a specific object in each class. For example: Jordan normal form is a canonical form for matrix similarity...

used to determine an "almost diagonal matrix" J {\displaystyle J} in Jordan normal form, similar to A {\displaystyle A} , which is useful in computing certain...

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...

number of results: The Jordan curve theorem, a topological result required in complex analysis The Jordan normal form and the Jordan matrix in linear algebra...

writing A = P J P − 1 {\displaystyle A=PJP^{-1}} , where J is in Jordan normal form, implies that A D = P J D P − 1 {\displaystyle A^{\text{D}}=PJ^{\text{D}}P^{-1}}...

mathematics, Jordan decomposition may refer to Hahn decomposition theorem, and the Jordan decomposition of a measure Jordan normal form of a matrix Jordan–Chevalley...

by the Jordan normal form theorem, which states that in this situation, A is similar to an upper triangular matrix of a very particular form. The simpler...

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...

diagonal. The Jordan normal form and the Jordan–Chevalley decomposition Applicable to: square matrix A Comment: the Jordan normal form generalizes the...

eigenvalues generalizes to the Jordan normal form. Over an algebraically closed field, any matrix A has a Jordan normal form and therefore admits a basis...

defective. (A diagonal matrix is a special case of the Jordan normal form with all trivial Jordan blocks of size 1 × 1 {\displaystyle 1\times 1} and is...

set of all m × n matrices over a field F denoted in this article Mmn(F) form a vector space. Examples of F include the set of rational numbers Q {\displaystyle...

polynomial Frobenius normal form Jordan normal form, up to a permutation of the Jordan blocks Index of nilpotence Elementary divisors, which form a complete set...

eigen-decomposition of a complex symmetric matrix A {\displaystyle A} , the Jordan normal form of A {\displaystyle A} may not be diagonal, therefore A {\displaystyle...

{\displaystyle \mathbf {A} } is a matrix over an algebraically closed field in Jordan normal form with respect to some basis, then A {\displaystyle \mathbf {A} } is...

{\displaystyle A} and wish to find a matrix J {\displaystyle J} in Jordan normal form, similar to A {\displaystyle A} , we are interested only in sets of...

polynomial). In this case A {\displaystyle A} is similar to a matrix in Jordan normal form. If A {\displaystyle A} and B {\displaystyle B} are two square n ×...

uniqueness of the principal square root can be deduced directly from the Jordan normal form (see below). An n×n matrix with n distinct nonzero eigenvalues has...

this form, it is called diagonalizable. More generally, and applicable to all matrices, the Jordan decomposition transforms a matrix into Jordan normal form...

algebra is reflexive if and only if the largest two blocks in the Jordan normal form of T differ in size by at most one. For example, the algebra { ( a...

Any normal matrix is similar to a diagonal matrix, since its Jordan normal form is diagonal. Eigenvectors of distinct eigenvalues of a normal matrix...

diagonal, and either ones or zeroes on the superdiagonal – known as Jordan normal form. Some matrices are not diagonalizable over any field, most notably...

and eigenspace Cayley–Hamilton theorem Spread of a matrix Jordan normal form Weyr canonical form Rank Matrix inversion, invertible matrix Pseudoinverse Adjugate...

Block diagonal matrices Shift matrices and shear matrices Matrices in Jordan normal form A skyline matrix, also called "variable band matrix" – a generalization...

a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of...

etc.). One can show that where J {\displaystyle J} is a matrix in Jordan normal form. By premultiplying by M − 1 {\displaystyle M^{-1}} , we obtain Note...

Eigenvalue perturbation Frobenius covariant Householder transformation Jordan normal form List of matrices Matrix decomposition Singular value decomposition...