instance normal matrices, is a special case of the Jordan normal form. The Jordan normal form is named after Camille Jordan, who first stated the Jordan decomposition...

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...

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...

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

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...

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}}...

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...

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...

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...

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...

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

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...

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...

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...

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...

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

{\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...

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 ×...

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

{\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...

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...

marginal stability can be analyzed by deriving the Jordan normal form: if and only if the Jordan blocks corresponding to poles with zero real part are...

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

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

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...

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

\left(2H_{ij}(0)\right).} The matrix (Hij(0)) can be recast in the Jordan normal form: (Hij(0)) = LJL−1, were L gives the desired non-singular linear transformation...

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...

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...

algebra Jordan normal form – Form of a matrix indicating its eigenvalues and their algebraic multiplicities Frobenius normal form – Canonical form of matrices...