SCALING POSITIVE DEFINITE MATRICES TO ACHIEVE PRESCRIBED EIGENPAIRS

被引：0

作者：

Hutchinson, George ^{[1
]}

机构：

[1] Mohawk Coll, 135 Fennell Ave W, Hamilton, ON, Canada

来源：

OPERATORS AND MATRICES | 2023年 / 17卷 / 04期

关键词：

Diagonal matrix scaling; positive definite matrices; doubly stochastic; Sinkhorn's theorem;

D O I：

10.7153/oam-2023-17-64

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the problem of scaling a given positive definite matrix A to achieve a prescribed eigenpair (lambda,v), by way of a diagonal scaling D*AD. We consider the case where D is required to be positive, as well as the case where D is allowed to be complex. We generalize a few classical results, and then provide a partial answer to a question of Pereira and Boneng regarding the number of complex scalings of a given 3 x 3 positive definite matrix A.

引用

页码：967 / 994

页数：28

共 12 条

[1] DIAGONAL EQUIVALENCE OF A NONNEGATIVE MATRIX TO A STOCHASTIC MATRIX [J].

BRUALDI, RA ;

PARTER, SV ;

SCHNEIDER, H .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1966, 16 (01) :31-&

[2]

DIETRICH O, 2016, Symmetric 3x3 matrices with repeated eigenvalues

[3]

GATHMANN A, 2018, Course Notes

[4] On the cardinality of complex matrix scalings [J].

Hutchinson, George .

SPECIAL MATRICES, 2016, 4 (01) :141-150

[5] On complex matrix scalings of extremal permanent [J].

Hutchinson, George .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 522 :111-126

[6]

Idel Martin., 2016, arXiv

[7] Scaling of symmetric matrices by positive diagonal congruence [J].

Johnson, Charles R. ;

Reams, Robert .

LINEAR & MULTILINEAR ALGEBRA, 2009, 57 (02) :123-140

[8] SCALING OF MATRICES TO ACHIEVE SPECIFIED ROW AND COLUMN SUMS [J].

MARSHALL, AW ;

OLKIN, I .

NUMERISCHE MATHEMATIK, 1968, 12 (01) :83-&

[9] REDUCTION OF A MATRIX WITH POSITIVE ELEMENTS TO A DOUBLY STOCHASTIC MATRIX [J].

MENON, MV .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 18 (02) :244-&

[10]

Parlett B.N., 1998, The Symmetric Eigenvalue Problem

← 1 2 →