### Abstract

Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂ^{n}, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

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

Pages (from-to) | 115-139 |

Number of pages | 25 |

Journal | Linear Algebra and Its Applications |

Volume | 252 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1997 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

### Cite this

*Linear Algebra and Its Applications*,

*252*(1-3), 115-139. https://doi.org/10.1016/0024-3795(95)00674-5

**The numerical range of 3 X 3 matrices.** / Keeler, Dennis S.; Rodman, Leiba; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 252, no. 1-3, pp. 115-139. https://doi.org/10.1016/0024-3795(95)00674-5

}

TY - JOUR

T1 - The numerical range of 3 X 3 matrices

AU - Keeler, Dennis S.

AU - Rodman, Leiba

AU - Spitkovsky, Ilya

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

AB - Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

UR - http://www.scopus.com/inward/record.url?scp=0039506402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039506402&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(95)00674-5

DO - 10.1016/0024-3795(95)00674-5

M3 - Article

VL - 252

SP - 115

EP - 139

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -