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Advanced Calculus: Difference between revisions
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==Implicit Function Theorem== | ==Implicit Function Theorem== | ||
==Line and Surface Integrals== | ==Line and Surface Integrals== | ||
==Derivatives with respect to vectors and matrices== | |||
Not typically covered in undergraduate analysis and calculus classes but necessary for machine learning.<br> | |||
See [https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf The Matrix Cookbook] | |||
* <math>\partial_{x} x^t x = \partial_{x} \operatorname{Tr}(x^t x) = \operatorname{Tr}( (\partial x)^t x + x^t (\partial x)) = 2 * \operatorname{Tr}(x^t (\partial x)) = 2x</math> | |||