Triangle InequalitiesThe triangle inequality for real and complex numbers are basic and appear in any analysis book.doi:10.1007/978-94-017-1043-5_17DS Mitrinovi'cJE Pevcari'cAM FinkSpringer Netherlands
Is it true that for a complex number z = x + jy: |x|≤|z|?Show it geometrically by representing z as a vector. (b) The so-called triangle inequality says that for any complex (or real) numbers z and v we have that |z+v|≤|z|+|v|Show a geometric example that verifies this...
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Proof. For if |A,B|≤ |B,C|, we have |∠ACB|°≤ |∠BAC|° by 4.1.1(i) and this result. The triangle inequality. If A,B,C are non-collinear points, then |C,A| < |A,B| + |B,C|. Proof. Take a point D so that B∈ [A,D] and |B,D| = |B,C|. As C,B⊂...
Triangle Inequality with Absolute Value:The triangle inequality with absolute value is another variation of the triangle inequality involving the sides of a triangle. It affirms that the following inequality holds for any two real numbers a and b: |a+b|≤|a|+|b|...
For the square function, if , then there is such that (1.2) The inequality (1.2) goes back to Paley [12], and has been reproved in many ways, for example, [2,3,4, 7, 10]. Its main application is in proving the -boundedness of martingale transforms (see [2]), that is, for...
The inequality constraints of equation (3) must apply, φi + ψit¯ ≤ 0 (18) where φi = Ei × U · ∆i and ψi = Ei × U · V for 0 ≤ i ≤ 2. 4.4 Pseudocode for the Query We have 8 subboundaries of the sphere-swept volume to test. For a fast no-intersection, ...
Keywordsandphrases.Triangleinequality,Diaz-Metcalfinequality,Reverseinequality,Com- plexinnerproductspace. 1 2SEVERS.DRAGOMIR assumptionsfortheimaginarypartIm x k ,a .ArefinementoftheDiaz-Metcalf resultisobtained.Applicationsforcomplexnumbersarepointedout. 2.TheCaseofaUnitVector Thefollowingresultholds. Theor...
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