✦ LIBER ✦

Relationships between partial orders of matrices and their powers

✍ Scribed by Jerzy K Baksalary; Jan Hauke; Xiaoji Liu; Sanyang Liu

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 190 KB
Volume: 379
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00535-4

No coin nor oath required. For personal study only.

✦ Synopsis

Baksalary and Pukelsheim [Linear Algebra Appl. 151 (1991)

135] considered the problem of how an order between two Hermitian nonnegative definite matrices A and B is related to the corresponding order between the squares A 2 and B 2 , in the sense of the star partial ordering, the minus partial ordering, and the Löwner partial ordering. In the present paper, possibilities of generalizing and strengthening their results are studied from two points of view: by widening the class of matrices considered and by replacing the squares by arbitrary powers.

📜 SIMILAR VOLUMES

Further relationships between certain pa

Further relationships between certain partial orders of matrices and their squares

✍ Jerzy K. Baksalary; Oskar Maria Baksalary; Xiaoji Liu 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 185 KB

Theorem 3 of Baksalary and Pukelsheim [Linear Algebra Appl. 151 (1991) 135] asserts that if both A and B are Hermitian nonnegative definite matrices, then the star order A \* B between them and the star order A 2 \* B 2 between their squares are equivalent and they imply the commutativity property A

On relationships between several classes

On relationships between several classes of Z-matrices, M-matrices and nonnegative matrices

✍ Reinhard Nabben 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 256 KB

Some Löwner partial orders of Schur comp

Some Löwner partial orders of Schur complements and Kronecker products of matrices

✍ Jianzhou Liu 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 320 KB

Partial orderings, preorderings, and the

Partial orderings, preorderings, and the polar decomposition of matrices

✍ Ju¨rgen Groβ; Jan Hauke; Augustyn Markiewicz 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 958 KB

Remarks on the sharp partial order and t

Remarks on the sharp partial order and the ordering of squares of matrices

✍ Jürgen Groß 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 113 KB

In this note we revisit the sharp partial order introduced by Mitra [S.K. Mitra, On group inverses and the sharp order, Linear Algebra Appl. 92 (1987) 17-37]. We recall some already known facts from certain matrix decompositions and derive new statements, relating our discussion to recent results in

Characterizations of minus and star orde

Characterizations of minus and star orders between the squares of Hermitian matrices

✍ Jerzy K Baksalary; Jan Hauke 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 167 KB

Groß [Linear Algebra Appl. 326 (2001) 215] developed characterizations of the minus and star partial orders between the squares of Hermitian nonnegative definite matrices referring to the concept of the space preordering. In the present paper, his results are generalized by deleting the nonnegative