scholarly journals Nonnegative persymmetric matrices with prescribed elementary divisors

2015 ◽  
Vol 483 ◽  
pp. 139-157 ◽  
Author(s):  
Ricardo L. Soto ◽  
Ana I. Julio ◽  
Mario Salas
Keyword(s):  
Elementary Divisors

scholarly journals On the Latent Roots of Certain Matrices

1928 ◽  
Vol 1 (2) ◽  
pp. 135-138 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Fundamental Theorem ◽  
Present Note ◽  
Principal Diagonal ◽  
Characteristic Determinant ◽  
Elementary Divisors ◽  
The Right ◽  
Latent Roots

In the present note certain known theorems on the latent roots of matrices are deduced from the fundamental theorem that a matrix A can be expressed in the form PQP-1, where P is non-singular and Q has zero elements everywhere to the left of the principal diagonal, and the latent roots of A in the diagonal. [The presence or absence of non-zero elements to the right of the diagonal is known to depend on the nature of the “elementary divisors” of the “characteristic determinant” of A, but in what follows these will not concern us.]

VI.—On Singular Pencils of Zehfuss, Compound, and Schläflian Matrices

1937 ◽  
Vol 56 ◽  
pp. 50-89 ◽  
Author(s):  
W. Ledermann
Keyword(s):  
Canonical Form ◽  
Direct Product ◽  
Canonical Forms ◽  
Singular Case ◽  
Elementary Divisors ◽  
Compound Matrices ◽  
Matrix Pencils ◽  
The Subject

In this paper the canonical form of matrix pencils will be discussed which are based on a pair of direct product matrices (Zehfuss matrices), compound matrices, or Schläflian matrices derived from given pencils whose canonical forms are known.When all pencils concerned are non-singular (i.e. when their determinants do not vanish identically), the problem is equivalent to finding the elementary divisors of the pencil. This has been solved by Aitken (1935), Littlewood (1935), and Roth (1934). In the singular case, however, the so-called minimal indices or Kronecker Invariants have to be determined in addition to the elementary divisors (Turnbull and Aitken, 1932, chap. ix). The solution of this problem is the subject of the following investigation.

Finite and infinite structures of rational matrices: a local approach

2015 ◽  
Vol 30 ◽  
Author(s):  
A. Amparan ◽  
S. Marcaida ◽  
Ion Zaballa
Keyword(s):  
Local Structure ◽  
Complete System ◽  
Irreducible Polynomial ◽  
Rational Functions ◽  
Rational Matrix ◽  
Local Approach ◽  
Elementary Divisors ◽  
Ring Of Polynomials ◽  
Principal Ideal Domains ◽  
Global And Local

The structure of a rational matrix is given by its Smith-McMillan invariants. Some properties of the Smith-McMillan invariants of rational matrices with elements in different principal ideal domains are presented: In the ring of polynomials in one indeterminate (global structure), in the local ring at an irreducible polynomial (local structure), and in the ring of proper rational functions (infinite structure). Furthermore, the change of the finite (global and local) and infinite structures is studied when performing a Mobius transformation on a rational matrix. The results are applied to define an equivalence relation in the set of polynomial matrices, with no restriction on size, for which a complete system of invariants are the finite and infinite elementary divisors.

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