Eugenio Beltrami

Eugenio Beltrami
Eugenio Beltrami
Born	(1835-11-16)16 November 1835 Cremona, Lombardy, Kingdom of Lombardy–Venetia, Austrian Empire
Died	18 February 1900(1900-02-18) (aged 64) Rome, Kingdom of Italy
Nationality	Italian
Alma mater	Ghislieri College, Pavia (no degree)
Known for	Beltrami equation Beltrami identity Beltrami's theorem Laplace–Beltrami operator Beltrami vector field Beltrami–Klein model
Scientific career
Fields	Mathematician
Institutions	University of Bologna University of Pisa University of Rome University of Pavia
Academic advisors	Francesco Brioschi
Doctoral students	Giovanni Frattini

Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times. Beltrami's use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.