A norm of linear transformation \(\Lambda : X \rightarrow Y\) is defined by \(\| \Lambda \| = \sup \{ \| \Lambda(x) \|:x \in X, \|x\| …

It is the main subject of analysis that finding conditions making sequential mathematical objects like a set, sequence, series to be …

The Fourier series represents a periodic function as a descrete vectors. The Fourier transformation turns a time domain non-periodic …

yaml --- mainfont: NanumGothic output: pdf_document: latex_engine: xelatex --- The mainfont is the LaTex option. The argument is a font …

Convolution is a vector operation on two vectors.
\[ Convolution \\ c * d = d*c \\ (c*d)_n = \Sigma_{i+j} c_i d_j = \Sigma_i c_i …

The optimization problem have two components that are objective function \(f_0 : \mathbb R ^n \rightarrow \mathbb R\) and the …

The purpose of approximation is finding optimal point \(x^*\) i.e. \(\nabla F(x^*) = 0\). 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), …

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