= James Joseph Sylvester
{c}
{title2=1814-1897}
{wiki}
<James Joseph Sylvester> was a <mathematician> whose work with <Arthur Cayley> helped develop <linear algebra> and <invariant theory>. He studied algebraic forms, their relations and quantities that detect special behavior of <polynomials>; his terminology included the <discriminant>.https://mathshistory.st-andrews.ac.uk/Biographies/Sylvester/[Biography, collaboration with Cayley and algebraic work of 1851–1853]{ref} His <Sylvester's law of inertia> explains why the numbers of positive and negative squares in a real <quadratic form> are unchanged by an invertible linear change of variables. Thus matrices that look different can describe the same underlying geometry, and the signs provide invariants that survive a change of coordinates.
Identity source: https://mathshistory.st-andrews.ac.uk/Biographies/Sylvester/
\Image[https://commons.wikimedia.org/wiki/Special:Redirect/file/James%20Joseph%20Sylvester%20by%20Alfred%20Edward%20Emslie.jpg?width=250]
{title=Portrait of <James Joseph Sylvester>}
{description=Alfred Edward Emslie (1848–1918), painted portrait dated 1889; reproduction sourced to Oxford Dictionary of National Biography, article 26872. PD-Art: original public domain in origin/life-plus-100-or-shorter jurisdictions; File also states pre-1931 United States publication. https://creativecommons.org/publicdomain/mark/1.0/[Source usage terms], via Wikimedia Commons.}
{source=https://commons.wikimedia.org/wiki/File:James_Joseph_Sylvester_by_Alfred_Edward_Emslie.jpg}
{width=250}
Back to article page
