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You are not logged in. #1 20060806 18:31:33
InequalitiesTriangle Inequality or CauchySchwarz Inequality Arithmetic, Geometric, and Harmonic Means In other words, if A, G, and H are the arithmetic, geometric, and harmonic means, respectively, then H ≤ G ≤ A. Hölder's Inequality where Chebyshev's Inequality For a_{1} ≥ a_{2} ≥ ... ≥ a_{n} and b_{1} ≥ b_{2} ≥ ... ≥ b_{n}, Minkowski's Inequality For positive a_{k}, b_{k} and p > 1, Bernoulli's Inequality For x > 1, x ≠ 0, and integers n > 1, A special case is Jensen's Inequality For 0 < p ≤ q and positive a_{k}, CauchySchwarz Inequality for Integrals Hölder's Inequality for Integrals where Minkowski's Inequality for Integrals For p > 1, Jensen's Inequality for Integrals For 0 < p < q, Young's Inequality Let f be a continuous strictly increasing realvalued function on [0, ∞), with f(0) = 0 and as x approaches ∞, f(x) approaches ∞. Then if g is the inverse function of f, for any positive numbers a, b we have Triangle Inequality for Vectors Schwarz's Inequality for Vectors CauchySchwarz Inequality for Inner Product Spaces Hadamard's Inequality Let A be an n × n matrix with entries a_{ij} and transpose A^{T}. Then Last edited by Zhylliolom (20060806 18:35:47) #2 20061001 17:15:15
Re: InequalitiesIt may be much better when equal conditions are given too. X'(yXβ)=0 