Triangle inequalityInner product spacesNormed spacesOstrowski inequalityIn this paper we obtain some inequalities related to the generalized triangle and quadratic triangle inequalities for vectors in inner product spaces. Some results that employ the Ostrowski discrete inequality for vectors in normed linear...
triangle inequality ,Mathematics. the theorem that the absolute value of the sum of two quantities is less than or equal to the sum of the absolute values of the quantities. the related theorem that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitude...
We know from the triangle inequality that (9.5)2||utv||⩽β−1||u||2+β||v||2. On substituting (9.5) into (9.4), one arrives at (9.2).□ 9.3.5 Young's inequality For any scalars ε>0,p>1, q=(1−p−1)−1>1 and vectors a∈ℜn and b∈ℜn, it follows that...
(analysis) The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors, or any equivalent inequality in other spaces. [..] + Add translation English-Chinese dictionary 三角不等式 noun the triangle inequality ...
Some inequalities in inner product spaces related to the generalized triangle inequality In this paper we obtain some inequalities related to the generalized triangle and quadratic triangle inequalities for vectors in inner product spaces. Some... S.S. Dragomir and Y.J. Cho and S.S. Kim - 《...
When x and y arereal numbers, they can be viewed as vectors in ℝ1,and the triangle inequality expresses a relationshipbetween absolute values.In Euclidean geometry, for right triangles the triangle inequality is a consequenceof the Pythagorean theorem, and for general triangles a consequence of...
we have inequality in the lines of pythagorean identity to test this. the triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side. let a, b and c are the lengths of the sides of triangle abc and c is the largest ...
Using the triangle inequality to accelerate k-means The k -means algorithm is by far the most widely used method for discovering clusters in data. We show how to accelerate it dramatically, while still always computing exactly the same result as the standard algorithm. The accelerated alg... ...
Triangle Inequality Theorem: The triangle inequality theorem states that the sum of any two sides of a triangle is greater than the third side. If this condition is not fulfilled, then such a triangle does not exist. Answer and Explanation: The given si...
For all triangles, angles and sides are related by the law of cosines and law of sines (also called the cosine rule and sine rule). The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side...