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PreprintCC BY-NC-ND 4.0arXiv

Zero-trace index of matrices

  • Kennett L. Dela Rosa
  • Eloise P. Misa
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Abstract

The zero-trace index t(A) of a square complex matrix A is introduced. It is defined as the largest integer k such that A admits a k × k compression with trace zero. This concept is analogous to the zero-dilation index d(A) and is closely related to the k-numerical range. The k-numerical range is characterized as an intersection of half-planes, which is used to derive a formula for t(A) that reduces its computation to the Hermitian case. Conditions for t(A) = d(A) are also established, and matrices satisfying t(A) = n − 1 are characterized. Finally, the zero-trace index is determined for several classes of matrices.

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Cite

BibTeXRIS
BibTeX
@misc{rosa2026zerotrace,
  title = {{Zero-trace index of matrices}},
  author = {Kennett L. Dela Rosa and Eloise P. Misa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24486},
  eprint = {2610.24486},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24486},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Zero-trace index of matrices
AU  - Kennett L. Dela Rosa
AU  - Eloise P. Misa
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24486
UR  - https://arxiv.org/abs/2610.24486
AB  - The zero-trace index t(A) of a square complex matrix A is introduced. It is defined as the largest integer k such that A admits a k × k compression with trace zero. This concept is analogous to the zero-dilation index d(A) and is closely related to the k-numerical range. The k-numerical range is characterized as an intersection of half-planes, which is used to derive a formula for t(A) that reduces its computation to the Hermitian case. Conditions for t(A) = d(A) are also established, and matrices satisfying t(A) = n − 1 are characterized. Finally, the zero-trace index is determined for several classes of matrices.
ER  -