Lecture 13: Global Illumination and Path Tracing (33)
amir656
If you broaden your concept of a vector, you can consider functions to be vectors and then you can write a matrix representation for linear operators like H and D given at the bottom. It just boils down to determining a basis for your domain, applying the operator to each element in said basis, then making a matrix where the ith column is equal to the operator applied to the ith element in the basis of the domain. For a much more rigorous and clear explanations of matrix representations, check out this video from the author of the Math 110 textbook:
https://www.youtube.com/watch?v=LlbzPlS3ZQk
If you broaden your concept of a vector, you can consider functions to be vectors and then you can write a matrix representation for linear operators like H and D given at the bottom. It just boils down to determining a basis for your domain, applying the operator to each element in said basis, then making a matrix where the ith column is equal to the operator applied to the ith element in the basis of the domain. For a much more rigorous and clear explanations of matrix representations, check out this video from the author of the Math 110 textbook: https://www.youtube.com/watch?v=LlbzPlS3ZQk