A square complex matrix A is said to be binormal if the associated matrices A*A and AA* commute. This matrix class yields a meaningful finite-dimensional extension of the concept of normality. The paper can be regarded as a survey of properties of binormal matrices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge (1991).
R. Bhatia, R. A. Horn, and F. Kittaneh, “Normal approximants to binormal operators,” Linear Algebra Appl., 147, 167–179 (1991).
M. R. Embry, “Conditions implying normality in Hilbert space,” Pacific J. Math., 18, 457–460 (1966).
M. R. Embry, “Similarities involving normal operators on Hilbert space,” Pacific J. Math., 35, 331–336 (1970).
S. L. Campbell, “Linear operators for which T * T and TT * commute,” Proc. Amer. Math. Soc., 34, 177–180 (1972).
S. L. Campbell, “Linear operators for which T * T and TT * commute (II),” Pacific J. Math., 53, 355–361 (1974).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 463, 2017, pp. 132–141.
Rights and permissions
About this article
Cite this article
Ikramov, K.D. Binormal Matrices. J Math Sci 232, 830–836 (2018). https://doi.org/10.1007/s10958-018-3912-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-018-3912-z