## Abstract

Let A be an n-by-n (n ≥ 2) S_{n} -matrix, that is, A is a contraction with eigenvalues in the open unit disc and with rank (I_{n} - A*A) = 1, and let W(A) denote its numerical range. We show that (1) if B is a k-by-k (1 ≤ k < n) compression of A, then W(B) ⊂≠ W(A), (2) if A is in the standard upper-triangular form and B is a k-by-k (1 ≤ k < n) principal submatrix of A, then ∂W(B) ∩ ∂W(A) = ∅, and (3) the maximum value of k for which there is a k-by-k compression of A with all its diagonal entries in ∂W(A) is equal to 2 if n = 2, and [n/2] if n≥3.

Original language | English |
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Pages (from-to) | 465-476 |

Number of pages | 12 |

Journal | Operators and Matrices |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - 2013 |

## Keywords

- Compression
- Numerical range
- S-matrix
- Unitary dilation

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