As a student geologist, I was never inducted into the world of linear algebra. Later, as a professional, I remained happily ignorant of Hessian matrices and Hermitian adjoints. But ever since reading Brian Russell's Don't neglect your math essay (Russell, 2012), I've wanted to put things right. In particular, I have wanted to understand the well-known geophysical equation at the heart of every inversion: d = Gm. It's only an equation — how hard can it be?

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