Chapter VIII Decomposition Theorems and the Jordan Canonical Form

Jordan Canonical Form for Finite Rank Elements in Jordan Algebras

Linear Algebra and its Applications ◽

10.1016/s0024-3795(96)00298-4 ◽

1997 ◽

Vol 260 (1-3) ◽

pp. 151-167

Author(s):

A LÃ³pez

Keyword(s):

Canonical Form ◽

Finite Rank ◽

Jordan Algebras ◽

Jordan Canonical Form ◽

Finite Rank Elements

A minimal property of the Jordan canonical form

Linear Algebra and its Applications ◽

10.1016/0024-3795(68)90024-4 ◽

1968 ◽

Vol 1 (4) ◽

pp. 503-510

Author(s):

Hans F. Bückner

Keyword(s):

Canonical Form ◽

Jordan Canonical Form ◽

Minimal Property

A Jordan canonical form for reachable linear systems

Linear Algebra and its Applications ◽

10.1016/0024-3795(89)90664-2 ◽

1989 ◽

Vol 122-124 ◽

pp. 489-524 ◽

Cited By ~ 3

Author(s):

D. Hinrichsen ◽

D. Prätzel-Wolters

Keyword(s):

Linear Systems ◽

Canonical Form ◽

Jordan Canonical Form

Nilpotent Matrices and the Jordan Canonical Form

State Space and Input-Output Linear Systems ◽

10.1007/978-1-4612-3816-4_12 ◽

1998 ◽

pp. 150-161

Author(s):

David F. Delchamps

Keyword(s):

Canonical Form ◽

Jordan Canonical Form ◽

Nilpotent Matrices

The general solution of x’ = Ax. The Jordan Canonical Form.

The Stability and Control of Discrete Processes - Applied Mathematical Sciences ◽

10.1007/978-1-4612-1076-4_8 ◽

1986 ◽

pp. 40-45

Author(s):

J. P. LaSalle

Keyword(s):

General Solution ◽

Canonical Form ◽

Jordan Canonical Form

Spectra inhabiting the left half-plane that are universally realizable

Special Matrices ◽

10.1515/spma-2021-0155 ◽

2021 ◽

Vol 10 (1) ◽

pp. 180-192

Author(s):

Ricardo L. Soto

Keyword(s):

Canonical Form ◽

Half Plane ◽

New Left ◽

Nonnegative Matrix ◽

Complex Numbers ◽

Jordan Canonical Form ◽

Positivity Condition ◽

Left Half ◽

Left Half Plane ◽

New Criteria

Abstract Let Λ = {λ1, λ2, . . ., λ n } be a list of complex numbers. Λ is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. Λ is universally realizable if it is realizable for each possible Jordan canonical form allowed by Λ. Minc ([21],1981) showed that if Λ is diagonalizably positively realizable, then Λ is universally realizable. The positivity condition is essential for the proof of Minc, and the question whether the result holds for nonnegative realizations has been open for almost forty years. Recently, two extensions of the Minc’s result have been proved in ([5], 2018) and ([12], 2020). In this work we characterize new left half-plane lists (λ1 > 0, Re λ i ≤ 0, i = 2, . . ., n) no positively realizable, which are universally realizable. We also show new criteria which allow to decide about the universal realizability of more general lists, extending in this way some previous results.

Cyclic Subspaces, Duality and the Jordan Canonical Form

Springer Undergraduate Mathematics Series - Linear Algebra ◽

10.1007/978-3-319-24346-7_16 ◽

2015 ◽

pp. 227-251

Author(s):

Jörg Liesen ◽

Volker Mehrmann

Keyword(s):

Canonical Form ◽

Jordan Canonical Form

AN ALGORITHM FOR OBTAINING THE JORDAN CANONICAL FORM OF A MATRIX

Software for Computer Control 1982 ◽

10.1016/b978-0-08-029352-3.50057-x ◽

1983 ◽

pp. 361-364

Author(s):

E.J. Moreno

Keyword(s):

Canonical Form ◽

Jordan Canonical Form

Matrix Diagonalization and Jordan Canonical Form

Algebraic and Differential Methods for Nonlinear Control Theory - Mathematical and Analytical Techniques with Applications to Engineering ◽

10.1007/978-3-030-12025-2_8 ◽

2019 ◽

pp. 109-123

Author(s):

Rafael Martínez-Guerra ◽

Oscar Martínez-Fuentes ◽

Juan Javier Montesinos-García

Keyword(s):

Canonical Form ◽

Jordan Canonical Form ◽

Matrix Diagonalization

The Jordan Canonical Form: an Old Proof

American Mathematical Monthly ◽

10.1080/00029890.1987.12000624 ◽

1987 ◽

Vol 94 (3) ◽

pp. 257-267 ◽

Cited By ~ 2

Author(s):

Richard A. Brualdi

Keyword(s):

Canonical Form ◽

Jordan Canonical Form