Pith. sign in

REVIEW 2 cited by

A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0502408 v1 pith:4ELBZH7N submitted 2005-02-18 math.CA

A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices

classification math.CA
keywords cauchycharacteristiceigenvaluesinterlacematrixpolynomialsymmetrictheorem
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

Cauchy's interlace theorem states that the characteristic polynomial of a symmetric matrix is interlaced by the characteristic polynomial of any principle submatrix. We prove this in two sentences using only the linearity of the determinant, and the fact that all eigenvalues of a symmetric matrix are real.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Emergence of generic first-passage time distributions for large Markovian networks

    cond-mat.stat-mech 2026-02 conditional novelty 7.0

    In the large-network limit, first-passage time distributions become deterministic when many generator eigenvalues contribute, and exponential when a single eigenvalue dominates.

  2. Weight-norm Criticality: A Mechanism for Loss Spikes Induced by the Normalization and Weight Decay

    cs.LG 2026-07 conditional novelty 5.0

    Weight decay on scale-invariant weights creates a norm-dependent sharpness boundary; crossing it predicts loss spikes in normalized networks.