The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms

DOI10.1016/0024-3795(93)00362-4zbMath0842.15011OpenAlexW2119459069WikidataQ94859381 ScholiaQ94859381MaRDI QIDQ1904047

James W. Demmel, Alan Edelman

Publication date: 4 August 1996

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://escholarship.org/uc/item/21t955zx

zbMATH Keywords

Jordan canonical formKronecker canonical formmatrix pencilelementary divisorsstaircase algorithmJordan canonical formsdimension of matricessuccessive range nullspace separations

Mathematics Subject Classification ID

Canonical forms, reductions, classification (15A21) Matrix pencils (15A22)

Related Items

Sensitivity and Computation of a Defective Eigenvalue, On the singular two-parameter eigenvalue problem. II, Rank-deficient matrices as a computational tool, Computation and presentation of graphs displaying closure hierarchies of Jordan and Kronecker structures, On the geometry of geometric rank, Defining functions for manifolds of matrices, Generic symmetric matrix pencils with bounded rank, Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree, The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits, Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade, Stratification of full rank polynomial matrices, Geometry of matrix polynomial spaces, Generic Eigenstructures of Hermitian Pencils, Computing nearby non-trivial Smith forms, Pencils of Quadrics: Old and New, Skew-symmetric matrix pencils: Codimension counts and the solution of a pair of matrix equations, Matrix polynomials with specified eigenvalues, First order spectral perturbation theory of square singular matrix pencils, Dimension of orbits of linear time-invariant singular systems under restricted system equivalence, Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade, The GSVD: Where are the Ellipses?, Matrix Trigonometry, and More, An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank, Formulas for Kronecker invariants using a representation theoretical approach, Robustness and perturbations of minimal bases. II: The case with given row degrees, Fixing multiple eigenvalues by a minimal perturbation, Estimating distances from quadruples satisfying stability properties to quadruples not satisfying them, A fast algorithm for index of annihilation computations, On the Sensitivity of Singular and Ill-Conditioned Linear Systems, The numerical Jordan form, On the structure of the solutions to the matrix equation \(G^\ast JG = J\), On bundles of matrix pencils under strict equivalence

Cites Work

• The codimension of singular matrix pairs
• The computation of Kronecker's canonical form of a singular pencil
• The generalized singular value decomposition and the general (A-\(\lambda\) B)-problem
• Kronecker's canonical form and the QZ algorithm
• RGSVD—AN Algorithm for Computing the Kronecker Structure and Reducing Subspaces of Singular $A - \lambda B$ Pencils
• The Jordan Canonical Form: An Old Proof
• Accurate Solutions of Ill-Posed Problems in control theory
• An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix
• The generalized eigenstructure problem in linear system theory
• Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form
• On a method of solving the complete eigenvalue problem for a degenerate matrix
• An algorithm for numerical determination of the structure of a general matrix
• ON MATRICES DEPENDING ON PARAMETERS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item