Related papers: A short proof of Cramer's theorem in R
A very short proof of Kneser's theorem via transversal is given.
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.
We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and…
In this technical note we provide a simple proof of Nehari's theorem on the optimal approximation by $H_\infty$ functions, based on convex duality.
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.
We give a short proof of the duality theorem for the reduced $L_p$-cohomology of a complete oriented Riemannian manifold.
We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…
This paper gives two different proofs to a structural theorem of decreasing minimization (lexicographic optimization) on integrally convex sets. The theorem states that the set of decreasingly minimal elements of an integrally convex set…
We give a short proof of the strong law of large numbers based on duality for random walk
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
We provide a simple proof of Kamp's theorem.
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
In this paper, we state the validity of Cramer's rule in a tropical context and its correspondence with classical Cramer's rule. This correspondence will allow us to prove a constructive version of Pappus' theorem conjectured in the paper…
In this short note we prove the convexity of minimizers of some variational problem in the Gauss space. This proof is based on a geometric version of an older argument due to Korevaar.
We present a short and self-contained proof of the choosability version of Brooks' theorem.
This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.