# Matrix of a linear transformation for an integral?

by marathon
Tags: integral, linear, matrix, transformation
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,691 Is there anything in your book about itegrals as linear transformations? Or about writing a general linear transformation as a matrix? Those are what you need here. An integral is a linear transformation: $\int af(x)+ bg(x)dx= a\int f(x)dx+ b\int g(x)dx$. To write a linear transformation from vector space U to vector space V, given ordered bases for each, do the following. Apply the linear transformation to the first vector in the ordered basis for U. That will be in V so can be written as a linear combination of the ordered basis for V. The coefficients of that linear combination will be the first column in the matrix. Do the same with the second vector in the ordered basis for U to get the second column, etc.