Talk:Weinstein–Aronszajn identity

Something is rather wrong here. At least references (2) and (3) are about an altogether different theorem (also about determinants, and also credited to Sylvester, which is presumably the reason for the confusion). Puffinry (talk) 10:53, 7 July 2012 (UTC)[reply]

I agree, Sylvester's determinant identity seems to be something else than the relation which is described on this page.Hedeberg (talk) 17:18, 21 August 2017 (UTC)[reply]

The result known as "Sylvester's determinant identity" is not this, but (see e.g., Wolfram's Mathworld) a generalization of the "Jacobi-Desnanot identity", and the reference^[1] concerns that result. The identity named here, incorrectly, as such, may well have been known to James Joseph Sylvester (and perhaps already to Jacobi), but is, in current literature, called the Weinstein-Aronszajn identity, because it was used in the setting of perturbations of the identity by trace class operators in infinite dimensions by these authors.Rphysicist (talk) 03:32, 22 June 2019 (UTC)[reply]

I have corrected the article to identify what is generally known as the Sylvester determinant identityRphysicist (talk) 01:11, 23 June 2019 (UTC)[reply]

References

^ Sylvester, James Joseph (1851). "On the relation between the minor determinants of linearly equivalent quadratic functions". Philosophical Magazine. 1: 295–305.
Cited in Akritas, A. G.; Akritas, E. K.; Malaschonok, G. I. (1996). "Various proofs of Sylvester's (determinant) identity". Mathematics and Computers in Simulation. 42 (4–6): 585. doi:10.1016/S0378-4754(96)00035-3.

[1] Sylvester, James Joseph (1851). "On the relation between the minor determinants of linearly equivalent quadratic functions". Philosophical Magazine. 1: 295–305.
Cited in Akritas, A. G.; Akritas, E. K.; Malaschonok, G. I. (1996). "Various proofs of Sylvester's (determinant) identity". Mathematics and Computers in Simulation. 42 (4–6): 585. doi:10.1016/S0378-4754(96)00035-3.

[1]