Matrix Calculus - Intro
Matrix Calculus Applied math very often involves matrix calculus. It is therefore a good idea to review some matrix calculus basics before diving into project specific solutions. It easier to learn the basics first and they are surprisingly simple to learn. A lot can be accomplished with a few intuitions and some notation. Tensors, matrices, vectors and scalars You can view all of these variables as tensors of differing rank. A rank $0$ tensor is scalar while a rank $1$ tensor is a vector and a rank $2$ tensor is a matrix. $$ \begin{array}{c c c} & tensor \ rank & example \\ scalar & 0 & x\\ vector & 1 & \begin{pmatrix} x_1 \\ x_2 \end{pmatrix} \\ matrix & 2 & \begin{pmatrix} x_{11} & x_{12} \\ x_{21} & x_{22} \end{pmatrix} \\ tensor & 3+ &\\ \end{array} $$ Vector and scalar valued functions We are likely all familiar with single valued functions of one variable : $$ f(x) $$ The value of the function $f$ depends on the i