Course Description
We all know that calculus courses such as 18.01 Single Variable Calculus and 18.02 Multivariable Calculus cover univariate and vector calculus, respectively. Modern …
We all know that calculus courses such as 18.01 Single Variable Calculus and 18.02 Multivariable Calculus cover univariate and vector calculus, respectively. Modern applications such as machine learning and large-scale optimization require the next big step, “matrix calculus” and calculus on arbitrary vector spaces.
This class covers a coherent approach to matrix calculus showing techniques that allow you to think of a matrix holistically (not just as an array of scalars), generalize and compute derivatives of important matrix factorizations and many other complicated-looking operations, and understand how differentiation formulas must be reimagined in large-scale computing.
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You may think you mastered derivatives after learning a few simple rules, but you could be bewildered if you are faced with more complicated functions like a matrix determinant (what is a derivative “with respect to a matrix”?), the solution of a differential equation, or other huge practical calculations. We address such topics by re-emphasizing what a derivative really is — linearization — and refocusing differential calculus on the linear algebra at its heart. (Image courtesy of Prof. Steven G. Johnson.)
