On the Necessary and Sufficient Condition for a Set of Matrices to Commute and Some Further Linked Results
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-08-17
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
This paper investigates the necessary and sufficient condition for a set of (real or complex) matrices to commute.
It is proved that the commutator [A,B]=0 for two matrices A and B if and only if a vector v(B) defined uniquely from the matrix B is in the null space of a well-structured matrix defined as the Kronecker sum A⊕(−A∗), which is always rank defective.
This result is extendable directly to any countable set of commuting matrices.
Complementary results are derived concerning the commutators of certain matrices with functions of matrices f(A) which extend the well-known sufficiency-type commuting result [A,f(A)]=0.
American Psychological Association (APA)
de La Sen, Manuel. 2009. On the Necessary and Sufficient Condition for a Set of Matrices to Commute and Some Further Linked Results. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-24.
https://search.emarefa.net/detail/BIM-488272
Modern Language Association (MLA)
de La Sen, Manuel. On the Necessary and Sufficient Condition for a Set of Matrices to Commute and Some Further Linked Results. Mathematical Problems in Engineering No. 2009 (2009), pp.1-24.
https://search.emarefa.net/detail/BIM-488272
American Medical Association (AMA)
de La Sen, Manuel. On the Necessary and Sufficient Condition for a Set of Matrices to Commute and Some Further Linked Results. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-24.
https://search.emarefa.net/detail/BIM-488272
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-488272
