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...
(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 ...
The Triangle Inequality Versus Projection onto a Dimension in Determining Cosine Similarity Neighborhoods of Non-negative Vectors. In Rough Sets and Current Trends in Computing; Yao, J., Yang, Y., Słowin´ ski, R., Greco, S., Li, H., Mitra, S., Polkowski, L., Eds.; Springer: ...
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...
In Euclidean geometry andsome other geometries, the triangle inequality is atheorem about distances, and it is written usingvectors and vector lengths (norms):where the length z of the third side has beenreplaced by the vector sum x + y. When x and y arereal numbers, they can be viewed...
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 ...
- 《Proceedings of the London Mathematical Society》 被引量: 16发表: 2016年 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 ...
Analysis of a hybrid PWM based on modified space vector and triangle comparison methods Classical space vector PWM with equal duration of application of zero state vectors V/sub 0/ and V/sub 7/ was modified. A factor-variable k/sub 0/ (proport... V Blasko - Ias Meeting 被引量: 715发...
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 side lengths of a triangle a...
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. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not...