Definition
The general formulation of covariance and contravariance refers to how the components of a coordinate vector transform under a change of basis (passive transformation). Thus let V be a vector space of dimension n over the field of scalars S, and let each of f = (X1,...,Xn) and f' = (Y1,...,Yn) be a basis of V. Also, let the change of basis from f to f′ be given by
-
(1)
for some invertible n×n matrix A with entries . Here, each vector Yj of the f' basis is a linear combination of the vectors Xi of the f basis, so that
Read more about this topic: Covariance And Contravariance Of Vectors Famous quotes containing the word definition:“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.” “Scientific method is the way to truth, but it affords, even in “The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.” |