Abdullah Sam Rouché-Frobenius theorem . In linear algebra, this theorem allows us to calculate the type of solutions of a system of linear equations based on the rank of the coefficient matrix and the rank of the extended matrix associated with the system. Summary …
The theorem Rolle is a proposition of the differential calculus which states that if a function of a real variable is derivable in the open interval I and continuous in the closure of I , then there is at …
Cosine theorem . In Geometry and more specifically in Euclidean geometry , it is a trigonometry theorem that in each triangle indicates the relationship between the proportion of the sum and the difference of the lengths of two sides with the …
Incompleteness Theorems . He asserts that, under certain conditions, no formal mathematical theory capable of describing natural numbers and arithmetic with sufficient expressiveness is both consistent and complete. That is, if the axioms of this theory do not contradict each other, …
The Hahn – Banach Theorem , in functional analysis especially, is a tool used in the problem of the prolongation of a linear functional, a fact that happens frequently. And if that is …
Fermat’s Last Theorem . It was formulated by Pierre de Fermat in 1637 and its proof was still achieved, 358 years after its proposal. The multi-century and multi-national effort to find proof of the conjecture …
Existence theorem . An existence theorem is a theorem that asserts that each of a wide range of problems has a solution of a particular type. A case could be this way: when …