Reverse-order law for the Moore-Penrose inverses of tensors

被引：25

作者：

Panigrahy, Krushnachandra ^{[1
]}

Behera, Ratikanta ^{[2
]}

Mishra, Debasisha ^{[1
]}

机构：

[1] Natl Inst Technol Raipur, Dept Math, Raipur, Chhattisgarh, India

[2] Indian Inst Sci Educ & Res Kolkata, Dept Math & Stat, Nadia, India

来源：

LINEAR & MULTILINEAR ALGEBRA | 2020年 / 68卷 / 02期

关键词：

Moore-Penrose inverse; tensor; matrix; Einstein product; reverse-order law; GENERALIZED INVERSES;

D O I：

10.1080/03081087.2018.1502252

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Reverse-order law for the Moore-Penrose inverses of tensors is useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverses of tensors. We then obtain a few necessary and sufficient conditions of the reverse-order law for the Moore-Penrose inverses of tensors via the Einstein product.

引用

页码：246 / 264

页数：19

共 22 条

[1] [Anonymous], 2007, COLLECTED PAPERS A E
[2] Barwick D.T., 1974, LINEAR ALGEBRA APPL, V8, P345
[3] BASKETT TS, 1969, LINEAR ALGEBRA APPL, V2, P87
[4] Further results on generalized inverses of tensors via the Einstein product
Behera, Ratikanta
Mishra, Debasisha
[J]. LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (08) : 1662 - 1682
[5] PSEUDO-INVERSE OF A PRODUCT
BOULDIN, R
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1973, 24 (04) : 489 - 495
[6] SOLVING MULTILINEAR SYSTEMS VIA TENSOR INVERSION
Brazell, M.
Li, N.
Navasca, C.
Tamon, C.
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2013, 34 (02) : 542 - 570
[7] Reverse order law of group inverses of products of two matrices
Cao, CG
Zhang, X
Tang, XM
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 158 (02) : 489 - 495
[8] Reverse order laws in C*-algebras
Cvetkovic-Ilic, Dragana S.
Harte, Robin
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (05) : 1388 - 1394
[9] Reverse order law for the group inverses
Deng, Chun Yuan
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 382 (02) : 663 - 671
[10] NOTE ON GENERALIZED INVERSE OF A MATRIX PRODUCT
GREVILLE, TN
[J]. SIAM REVIEW, 1966, 8 (04) : 518 - &

← 1 2 3 →