GENERALIZED HIGHER-RANK NUMERICAL RANGE

Authors

Abstract:

In this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

GENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE

The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...

full text

generalized higher-rank numerical range

in this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

full text

generalized joint higher-rank numerical range

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

full text

Multiaccess quantum communication and product higher rank numerical range

In the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range [M.–D. Choi et al., Rep. Math. Phys. 58, 77 (2006); Lin. Alg. Appl. 418, 828 (2006)], is a natural tool for studying a construction of quantum error correction codes for multiple access channels. We review properties of this set and relate it to o...

full text

Some Results on the Generalized Higher Rank Numerical Ranges

In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for > 0, the notion of Birkhoff-James approximate orthogonality sets for −higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural general...

full text

On higher rank numerical hulls of normal matrices

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 1  issue 2

pages  163- 168

publication date 2012-03-11

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023