A great many of the calculations we do in science and engineering are really matrix multiplication in disguise. The first goal of this chapter is to unmask the disguise by showing many examples. Second, we will illuminate the meaning of the adjoint operator （伴随算子）(matrix transpose) in these many examples. Geophysical modeling calculations generally use linear operators that predict data from models. Our usual task is to find the inverse of these calculations, i.e., to find models (or make maps) from the data. Logically, the adjoint is the first step and a part of all subsequent steps in this inversion process. Surprisingly, in practice the adjoint sometimes does a better job than the inverse! This is because the adjoint operator tolerates imperfections in the data and does not demand that the data provide full information. Using the methods of this chapter, you will find that once you grasp the relationship between operators in general and their adjoints, you can have the adjoint just as soon as you have learned how to code the modeling operator.

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