### Abstract

For the classical numerical radius r(A) of an n-by n real or complex matrix A, we consider inequalities of the following two types: r(f(A)) ≤ f(r(A)); and r(f(A)g(A)) ≤ r(f(A))r(g(A)) in which f and g are polynomials. In the latter case, the event in which f and g are simple powers is of special interest. We present a variety of particular results depending upon the dimension n and the classification of A or the polynomials. A number of natural questions remain open

Original language | English (US) |
---|---|

Pages (from-to) | 13-24 |

Number of pages | 12 |

Journal | Linear and Multilinear Algebra |

Volume | 37 |

Issue number | 1-3 |

DOIs | |

State | Published - Jun 1 1994 |

### ASJC Scopus subject areas

- Algebra and Number Theory

## Fingerprint Dive into the research topics of 'Inequalities Involving the Numerical Radius'. Together they form a unique fingerprint.

## Cite this

Johnson, C. R., Spitkovsky, I. M., & Gottlieb, S. (1994). Inequalities Involving the Numerical Radius.

*Linear and Multilinear Algebra*,*37*(1-3), 13-24. https://doi.org/10.1080/03081089408818310