Open AccessA Proof of the Sylvester Criterion for Quadratic Forms via Optimality Conditions for Quadratic Functions
Author(s) -
Giorgio Giorgi
Publication year - 2022
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v14n2p1
Subject(s) - mathematics , quadratic equation , quadratic function , definite quadratic form , quadratic form (statistics) , isotropic quadratic form , binary quadratic form , sylvester's law of inertia , legendre symbol , sylvester matrix , quadratic programming , pure mathematics , combinatorics , mathematical analysis , mathematical optimization , symmetric matrix , geometry , polynomial , eigenvalues and eigenvectors , physics , matrix polynomial , quantum mechanics , polynomial matrix
We give a proof of the so-called Sylvester criterion for quadratic forms (for real symmetric matrices), based on elementary optimality properties of quadratic functions.