pca1.tex

\documentclass{article}
\usepackage{tikz, pgfplots}
\usetikzlibrary{calc}

\begin{document}
  \centering
  \begin{tikzpicture}
    \coordinate (Origin)   at (0,0);
    \coordinate (XAxisMin) at (-0.5,0);
    \coordinate (XAxisMax) at (2.5,0);
    \coordinate (YAxisMin) at (0,-0.5);
    \coordinate (YAxisMax) at (0,4.5);
    \coordinate (PStart) at (-1.5,4);
    \coordinate (PEnd) at (6, 4);
    \coordinate (kuStart) at (0, 4);
    \coordinate (kuEnd) at (5, 4);
    \coordinate (uEnd) at (2, 0);
    \coordinate (xPoint) at (2, 6);
    
    \draw [->, thin, gray] (XAxisMin) -- (XAxisMax);% Draw x axis
    \draw [->, thin, gray] (YAxisMin) -- (YAxisMax);% Draw y axis
    \draw [black] (PStart) -- (PEnd) node at (-1.3,4.25) {$L$};
    \draw [red, ultra thick, -latex] (kuStart) -- (kuEnd);
    \draw [red, ultra thick, -latex] (Origin) -- (kuStart) 
    node [black] at (-0.25, 2) {$\mathbf{v}$};
    \draw [red, ultra thick, -latex] (Origin) -- (kuEnd) 
    node [black, rotate = 38] at (2.2, 2.1) {$(\mathbf{u}^T\mathbf{x})\cdot \mathbf{u} + \mathbf{v}$};
    \draw [red, ultra thick, -latex] (Origin) -- (uEnd) 
    node [black] at (2, -0.25) {$\mathbf{u}$};
    \draw [black, dashed] (xPoint) -- (2, 4)
    node at (2.25, 6) {$\mathbf{x}$};
    \filldraw [red] (xPoint) circle (2pt);
    \draw (2, 4) rectangle (2.2, 4.2);
    \draw [->] (2, 4) .. controls (2.5, 5.5) and (3.5, 5.9) .. (4, 6)
    node[right] {$Proj = (\mathbf{u}^T\mathbf{x})\mathbf{u}$};
  \end{tikzpicture}
\end{document}