# Eugenio Beltrami

## Italian mathematician / From Wikipedia, the free encyclopedia

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**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.

**Quick facts: Eugenio Beltrami, Born, Died, Nationality, Al...**▼

Eugenio Beltrami | |
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Born | (1835-11-16)16 November 1835 |

Died | 18 February 1900(1900-02-18) (aged 64) |

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 |

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