bibkey: hornjohnson2012matrixanalysis
authors: Roger A. Horn and Charles R. Johnson
year: 2012
title: Matrix Analysis
doi: 10.1017/CBO9781139020411
claim: Fischer's inequality bounds the determinant of a positive definite matrix by the product of the determinants of its principal diagonal blocks.
strata_touched:
  - D5/S3/Arith/GoldenResource/IntegerFischerSelector
license: citation-only
triage: anchor

Matrix Analysis

Second edition, Cambridge University Press.

Fischer’s inequality compares a positive definite matrix with its principal diagonal blocks. Taking one block of order two and all remaining blocks of order one gives the determinant bound formalized here. The integer loss and the logarithmic selector estimate are subsequent arithmetic deductions.

Verified locator

• DOI: https://doi.org/10.1017/CBO9781139020411
• Secondary statement and locator: https://en.wikipedia.org/wiki/Fischer%27s_inequality
• Checked on 2026-09-08: the secondary source states Fischer’s inequality, its extension to multiple principal diagonal blocks, and the connection with Hadamard’s inequality; it cites Theorem 7.8.5 in Horn and Johnson.
• The book’s primary page was not inspected in this attempt. The locator above is a secondary-source locator, not a claim of direct page inspection.