\subsection{Question 6} Let $v=\begin{pmatrix}x\\y\end{pmatrix}$ be the least squares solution to the equation.Then we have:\begin{align*} & A^TAv = A^Tb\\ &\implies\begin{pmatrix}1&-1&2\\1&1&1\end{pmatrix}\begin{pmatrix}1&1\\-1&1\\2&1\end{pmatrix}\begin{pmatrix...
Each of the crosses (as well as the numbers, although that is not so important) should be centred at the centre of their each squares. As you can see in the example below, I have tried both using \rputand uput, but neither seems to work. One provides correctly the x-coordinate, wh...
\documentclass{article} % for example images \usepackage{mwe} \usepackage[labelformat=simple]{subcaption} \begin{document} \renewcommand*{\thesubfigure}{\thefigure.\arabic{subfigure}} \makeatletter \renewcommand{\p@subfigure}{} \makeatother \begin{figure} \begin{minipage}{0.8\textwidth}% \incl...
This repo is to hold the public dataset for EquationGPT, which aims to collect Equation related Q&A corpus to finetune foundation models of GPT/ChatGPT. Each prompt-completion pairs contains information about the latex code for the equation, the meaning of each symbols, and related materials. ...
Next: Overview of LaTeX, Previous: LaTeX2e: An unofficial reference manual, Up: LaTeX2e: An unofficial reference manual [Contents][Index] 1 About this document This is an unofficial reference manual for the LaTeX2e document preparation system, which is a macro package for the TeX typesetting ...
The second and third examples show the validity and feasibility of the proposed results for PFTDS with the same or fewer rule numbers of the polynomial fuzzy controller. 展开 关键词: Stability analysis Nonlinear systems Asymptotic stability Delays Fuzzy systems Numerical stability Linear matrix ...
from each MLP/PR10 protein-containing sample. Each data set was scaled so that the maximum observed fluorescence corresponded to 100% and individual data points were plotted, and a rectangular hyperbolic ligand binding function was fit, using least-squares analysis (Prism 5 software, Graphpad, USA...
Find the least squares esimator for \(\hat{\beta_1}\) for the slope \(\beta_1\). \\ \solution To find the least squares estimator, we should minimize our Residual Sum of Squares, RSS: \[ \begin{split} RSS &= \sum_{i = 1}^{n} {(Y_i - \hat{Y_i})}^2 \\ &= \sum...
Opium poppy accumulates copious amounts of several benzylisoquinoline alkaloids including morphine, noscapine, and papaverine, in the specialized cytoplasm of laticifers, which compose an internal secretory system associated with phloem throughout the pl
I would like to transform in MathJAx a matrix of numbers into the matrix where entries are color squares. The example of this could be the textbelowhowever it has a drawback that it has inserted vertical and horizontal spaces between squares. ...