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The optimization problem have two components that are objective function $f_0:R^n\to R$ and the …

The purpose of approximation is finding optimal point $x^{\ast }$ i.e. $\nabla F\left(x^{\ast }\right)=0$. We need a step/search direction $\Delta x$ …

Bases are the central idea of linear algebra. An invertable square matrix has eigenvectors. A symetric matrix has orthogonal …

This is a note for part III of Linear Algebra and learning from data, Gilbert Strang The main themes are sparsity (Low rank), …

Differential equations describe the change of state. The change relates to the state. The solutions of the differential equations are …

Information relates to uncertainty. The Shannon information content of an outcome $x$ is $h\left(x\right)=-lo{g}_{2}P\left(x\right)$. The rare event has …

$$f\left(x\right)=\sum _{k=0}^{\infty }{c}_k{x}^k=c_0+c_{1}x+c_2{x}^2+\cdots .$$ This is an approximation that is a function of h and …