Eugène Rouché (18 August 1832 – 19 August 1910) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
.
Career
He was an alumnus of the
École Polytechnique
(, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris.
The school was founded in 1794 by mat ...
, which he entered in 1852. He went on to become professor of mathematics at the Charlemagne lyceum then at the
École Centrale, and admissions examiner at his alma mater. He is best known for
Rouché's theorem
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions and holomorphic inside some region K with closed contour \partial K, if on \partial K, then and have the same number of zeros inside K, where ...
in
complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...
, which he published in his alma mater's institutional journal in 1862, and for the
Rouché–Capelli theorem
Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions of a system of linear equations, given the ranks of its augmented matrix and coefficient matrix. The theorem is variously known as the:
* Rouché†...
in
linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrix (mathemat ...
.
His son,
Jacques
Jacques or Jacq are believed to originate from the Middle Ages in the historic northwest Brittany region in France, and have since spread around the world over the centuries. To date, there are over one hundred identified noble families related t ...
, was a noted patron of the arts who managed the
Paris Opera
The Paris Opera ( ) is the primary opera and ballet company of France. It was founded in 1669 by Louis XIV as the , and shortly thereafter was placed under the leadership of Jean-Baptiste Lully and officially renamed the , but continued to be kn ...
for thirty years (1914–1944).
See also
*
Rouché's theorem
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions and holomorphic inside some region K with closed contour \partial K, if on \partial K, then and have the same number of zeros inside K, where ...
*
Rouché–Capelli theorem
Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions of a system of linear equations, given the ranks of its augmented matrix and coefficient matrix. The theorem is variously known as the:
* Rouché†...
References
* Rouché et Comberousse (de), Traité de géométrie, tomes I et II, 7e édition, 1900 (réédition Jacques Gabay 1997).
External links
Biography at the St Andrews university website
1832 births
1910 deaths
People from Gard
École Polytechnique alumni
Academic staff of École Polytechnique
19th-century French mathematicians
Members of the French Academy of Sciences
Members of the Ligue de la patrie française
{{France-mathematician-stub