Kaddison generalized this result to self-adjoint normal elements in a unital positive map. This result can be used to show that the covariance of a pair of random variables is less than the square root of the product of their variances, and one generalization of it is expressed in terms of functions
Kaddison generalized this result to self-adjoint normal elements in a unital positive map. This result can be used to show that the covariance of a pair of random variables is less than the square root of the product of their variances, and one generalization of it is expressed in terms of functions on L-p spaces and is named for Holder. Also applicable to integrals rather than sums, one proof of this result on Euclidean spaces involves rearranging and finding the discriminant of a quadratic polynomial. It is used in the proof of the Heisenberg uncertainty principle, and for a sequence of length 2 it can be reduced to the triangle inequality. For 10 points, name this result that essentially states that the inner product of two vectors is less than the product of their norms, an inequality named for two guys.
Kaddison generalized this result to self-adjoint normal elements in a unital positive map.
{Cauchy-Schwarz} inequality