scholarly journals Inequalities for permanents and permanental minors of row substochastic matrices

2019 ◽  
Vol 35 ◽  
pp. 633-643
Author(s):  
Zhi Chen ◽  
Jiawei Li ◽  
Lizhen Yang ◽  
Zelin Zhu ◽  
Lei Cao
Keyword(s):  
Identity Matrix ◽  
Permanent Function

In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.

Inequalities for permanents and permanental minors

1965 ◽  
Vol 61 (3) ◽  
pp. 741-746 ◽  
Author(s):  
R. A. Brualdi ◽  
M. Newman
Keyword(s):  
Convex Function ◽  
Convex Set ◽  
Identity Matrix ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Counter Example ◽  
Doubly Stochastic Matrices ◽  
Permanent Function ◽  
Image Position

Let Ωndenote the convex set of alln×ndoubly stochastic matrices: chat is, the set of alln×nmatrices with non-negative entries and row and column sums 1. IfA= (aij) is an arbitraryn×nmatrix, then thepermanentofAis the scalar valued function ofAdefined bywhere the subscriptsi1,i2, …,inrun over all permutations of 1, 2, …,n. The permanent function has been studied extensively of late (see, for example, (1), (2), (3), (4), (6)) and it is known that ifA∈ Ωnthen 0 <cn≤ per (A) ≤ 1, where the constantcndepends only onn. It is natural to inquire if per (A) is a convex function ofAforA∈ Ωn. That this is not the case was shown by a counter-example given by Marcus and quoted by Perfect in her paper ((5)). In this paper, however, she shows that per (½I+ ½A) ≤ ½ + ½ per (A) for allA∈ Ωn. HereI=Inis the identity matrix of ordern.

scholarly journals The monotonicity of the permanent function

1991 ◽  
Vol 91 (1) ◽  
pp. 99-104 ◽  
Author(s):  
Suk Geun Hwang
Keyword(s):  
Permanent Function

Remark on algorithm 361 [G6]: permanent function of a square matrix I and II

1970 ◽  
Vol 13 (6) ◽  
pp. 376
Author(s):  
Bruce Shriver ◽  
P. J. Eberlein ◽  
R. D. Dixon
Keyword(s):  
Permanent Function ◽  
Square Matrix

scholarly journals Toeplitz Operators with Lagrangian Invariant Symbols Acting on the Poly-Fock Space of ℂ n

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jorge Luis Arroyo Neri ◽  
Armando Sánchez-Nungaray ◽  
Mauricio Hernández Marroquin ◽  
Raquiel R. López-Martínez
Keyword(s):  
Toeplitz Operators ◽  
Complex Space ◽  
Fock Space ◽  
Identity Matrix ◽  
The Matrix

We introduce the so-called extended Lagrangian symbols, and we prove that the C ∗ -algebra generated by Toeplitz operators with these kind of symbols acting on the homogeneously poly-Fock space of the complex space ℂ n is isomorphic and isometric to the C ∗ -algebra of matrix-valued functions on a certain compactification of ℝ n obtained by adding a sphere at the infinity; moreover, the matrix values at the infinity points are equal to some scalar multiples of the identity matrix.

The Permanent Function (PERMAN)

1978 ◽  
pp. 217-225
Author(s):  
ALBERT NIJENHUIS ◽  
HERBERT S. WILF
Keyword(s):  
Permanent Function

8. Matrices and groups

2015 ◽  
pp. 101-110
Author(s):  
Peter M. Higgins
Keyword(s):  
Dihedral Group ◽  
Inverse Matrix ◽  
Identity Matrix ◽  
Matrix Products ◽  
Square Matrix

‘Matrices and groups’ continues with the example of geometric matrix products to see what happens when we compose the mappings involved. It explains several features, including the identity matrix, the inverse matrix, the square matrix, and the concept of isomorphism. If a collection of matrices represent the elements of a group, such as the eight matrices that represent the dihedral group D, then each of these matrices A will have an inverse, A −1, such that AA-1 = A-1A =I, the identity matrix. This prompts the twin questions of when the inverse of a square matrix A exists and, if it does, how to find it.

Commutators of Matrices with Prescribed Determinant

1968 ◽  
Vol 20 ◽  
pp. 203-221 ◽  
Author(s):  
R. C. Thompson
Keyword(s):  
Finite Field ◽  
Multiplicative Group ◽  
Companion Matrix ◽  
Identity Matrix ◽  
Commutative Field

Let K be a commutative field, let GL(n, K) be the multiplicative group of all non-singular n × n matrices with elements from K, and let SL(n, K) be the subgroup of GL(n, K) consisting of all matrices in GL(n, K) with determinant one. We denote the determinant of matrix A by |A|, the identity matrix by In, the companion matrix of polynomial p(λ) by C(p(λ)), and the transpose of A by AT. The multiplicative group of nonzero elements in K is denoted by K*. We let GF(pn) denote the finite field having pn elements.

When is a Matrix Positive

1974 ◽  
Vol 17 (3) ◽  
pp. 409-410
Author(s):  
Daniel Brand
Keyword(s):  
Complex Numbers ◽  
Identity Matrix ◽  
Conjugate Transpose

Throughout this note we shall use the following conventions and notations: All matrices have entries in the field of complex numbers. I denotes the identity matrix with compatible dimensions. A* is the conjugate transpose of a matrix A. A being self adjoint means A = A*.

scholarly journals Note on best possible bounds for determinants of matrices close to the identity matrix

2015 ◽  
Vol 466 ◽  
pp. 21-26 ◽  
Author(s):  
Richard P. Brent ◽  
Judy-anne H. Osborn ◽  
Warren D. Smith
Keyword(s):  
Identity Matrix
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