The Rouche-Capelli Theorem is a result of linear algebra that determines the number of solutions of a system of linear equations from the ranks of its coefficient matrix and its augmented matrix. The same result is known under several other names depending on country, including the Kronecker-Capelli theorem, the Rouche-Fontene theorem, the Rouche-Frobenius theorem, and simply the Frobenius theorem.
Facts
StatementA system of linear equations with n variables and coefficients in a field K has a solution if and only if its coefficient matrix A and its augmented matrix [A|b] have the same rank. 1 Classification
Statement Form Statement FormCharacterization Theorem 1 Connections
Associated With
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Rouche-Capelli theorem (Wikipedia)
StatementQuote, Statement
has a solution if and only if its coefficient matrix A and its augmented matrix [A|b] have the same rank
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.