Determinants are certain complicated functions of square matrices (or, equivalently, of their column vectors or of their entries). Their usefulness follows mainly from two of their properties: first, they can be used to compute areas and volumes and second, a zero determinant characterizes singular matrices. Computing areas and volumes brings determinants into the formulas for changing variables in multiple integrals, and their vanishing for singular matrices is at the heart of Chapter 7 for evaluating what are called eigenvalues of matrices, which occur in many geometrical and physical applications.
KeywordsCross Product Coriolis Force Area Function Standard Vector Edge Vector
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