Rouché–Capelli theorem
Existence of solutions for a system of linear equations in terms of matrix ranks / From Wikipedia, the free encyclopedia
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Not to be confused with Rouché's theorem.
In linear algebra, the Rouché–Capelli theorem determines the number of solutions for a system of linear equations, given the rank 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, Croatia, Romania, Serbia and Russia;
- Rouché–Fontené theorem in France;
- Rouché–Frobenius theorem in Spain and many countries in Latin America;
- Frobenius theorem in the Czech Republic and in Slovakia.