Rouché–Capelli theorem

Not to be confused with Rouché's 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–Capelli theorem in English speaking countries, Italy and Brazil;
  • Kronecker–Capelli theorem in Austria, Poland, Ukraine, Bosnia, Croatia, Romania, Serbia and Russia;
  • Rouché–Fontené theorem in France;
  • Rouché–Frobenius theorem in Spain and many countries in Latin America;
  • Frobenius theorem in Czechia and Slovakia.
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