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Linearity
From Mathematics Is A Science
Revision as of 14:26, 30 July 2012 by imported>WikiSysop
Preserving vector operations:
- scalar multiplication: $f(ax) = ax$, and
- addition: $f(x + y) = f(x) + f(y)$.
A linear operator then is determined by its values on the elements of the basis of the domain space, as they are expressed as linear combinations of the elements of the basis of the target space. The coefficients of these linear combinations form the columns of the matrix of linear operator.