在表中插入多个矩阵

在表中插入多个矩阵

在表格的第四行中,如何将第一列的元素与第二列对齐,如图所示? 在此处输入图片描述

\documentclass[a4paper,english,12pt,oneside]{book}
%\documentclass[11pt,draft]{article}
%\usepackage{fullpage}
%\usepackage[top=1in, bottom=1in, left=1in, %right=1in]{geometry}
%\usepackage[margin=1in, paperwidth=8.5in, paperheight=11in]{geometry}
%\usepackage[left=2cm, right=2cm, top=2.5cm, bottom=2.5cm]{geometry}
\usepackage[left=20mm]{geometry}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{graphicx}
\usepackage{refstyle}
\usepackage{subcaption}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{enumerate}
\usepackage{epstopdf}
\usepackage{breqn}
\usepackage{mathtools}
%-------------------------------------------------------------------------------
%\usepackage{a4wide}
\usepackage{amsfonts}
\usepackage{amstext}
\usepackage{amsthm}
\usepackage{newlfont}
\usepackage{graphics}
\usepackage{tabularx}
\usepackage{geometry}
\usepackage{lscape}
\usepackage{multirow}
\usepackage{epsfig}
\usepackage{bm,amsmath}
%----------------------------------------------------
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{pifont}
%\usepackage[lite]{mtpro2}
%-----------------------------------------------------
\usepackage{color}
\definecolor{violet}{rgb}{0.7,0.2,0.8}
\definecolor{bluevert}{rgb}{0,0.9,1}
\definecolor{trustcolor}{rgb}{0.71,0.14,0.07}
\definecolor{PinkTriton}{rgb}{.708 ,.055 ,.275}
\definecolor{RedTriton}{rgb}{.491 ,.097 ,.066} % couleur rouge du triton
\definecolor{OrangeTriton}{rgb}{.953 ,.502 ,.04}
%-------------------------------------------------------------------------------
\usepackage[colorlinks=true,linkcolor=blue, citecolor=blue]{hyperref}
%===============================================================================
  \newcommand*{\rowvec}[1]{\left[ #1\right]}


\renewcommand{\vec}[1]{\bm{#1}}
\newcommand{\mat}[1]{\bm{#1}}
\newcommand{\tran}{^{\mathstrut\scriptscriptstyle\top}} 
\setlength\parindent{0pt}
%--------------------------------------------------------
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{#1}}
\makeatother
%--------------------------------------------------------


\begin{document}

\tabref{dif_irm_tep}).
\begin{table}[ht!]
\centering
  \begin{tabular}{|l|l|}
  \hline
  \multicolumn{2}{|l|}{Step2. Apply numerically stable ASR filter}\\
  \hline
  2a. 2.b & Given $ A = \begin{bmatrix}[ccc|c] \theta^5/20 & \theta^4/8 & \theta^3/6 & \theta^3/3\\ \theta^4/8 & \theta^3/3 & \theta^2/2 & \theta^2/2\\ \theta^3/6 & \theta^2/2 & \theta & 1 \end{bmatrix} $,$ A|_{\theta = 2}\begin{bmatrix}[ccc|c] 1.6000 & 2.0000 & 1.3333 & 2.6667\\ 2.0000 & 2.6667 & 2.0000 & 2.0000\\ 1.3333 & 2.0000 & 2.0000 & 1 \end{bmatrix}$.
  compute $ R = \begin{bmatrix}[ccc|c] −3.8788 & 2.0000 & −3.0476 & −3.3247\\ 0 & −0.2576 & −0.6954 & 0.8886\\ 0 & 0 & 0.0797 & 0.5179 \end{bmatrix} $ where $ Q = \begin{bmatrix} −0.5541 & 0.0773 & −0.4618 \\ 0.5795 & −0.2576 & −0.8113 \\ 0.5976 & −0.7171 & 0.3586 \end{bmatrix}$ \\ 
   \hline
  \multicolumn{2}{|l|}{Step3. computation of the derivation of the ASR filter (p=1)}\\  
  \hline
  3a. 3b. 3c. 3d, 3e. & Given $ A_{\theta}{'} = \begin{bmatrix}[ccc|c] \theta^4/4 & \theta^3/2 & \theta^2/2 & \theta^2\\ \theta^3/2 & \theta^2 & \theta & \theta\\ \theta^2/2 & \theta & 1 & 0 \end{bmatrix} $. So $ A_{\theta}{'}|_{\theta = 2} = \begin{bmatrix}[ccc|c] 4 & 4 & 2 & 4\\ 4 & 4 & 2 & 2\\ 2 & 2 & 1 & 0 \end{bmatrix} $. compute $QA_{\theta}{'}$. Denote $X_1 = \begin{bmatrix} −5.9105 & −5.9105 & −2.9552 \\ 1.0045 & 1.0045 & 0.5022 \\ 0.2390 & 0.2390 & 0.1195 \end{bmatrix} $,$N_1 = \begin{bmatrix} −3.6017 \\ 2.4725 \\ 0.9562 \end{bmatrix}$. Find $X_1R{11}^{-1} = \begin{bmatrix} 2.0469 & −7.8778 & −27.5511 \\ −0.3479 & 1.3388 & 4.6822 \\ −0.0828 & 0.3186 & 1.1143 \end{bmatrix}$. Split it into $L_1 = \begin{bmatrix} 0 & 0 & 0 \\ −0.3479 & 0 & 0 \\ −0.0828 & 0.3186 & 0 \end{bmatrix}$, $D_1 = \begin{bmatrix} 2.0469 & 0 & 0 \\ 0 & 1.3388 & 0 \\ −0.0828 & 0 & 0 \end{bmatrix}$, $U_1 = \begin{bmatrix} 0 & −7.8778 & −27.5511 \\ 0 & 0 & 4.6822 \\ 0 & 0 & 0 \end{bmatrix}$  \\
\hline
 \multicolumn{2}{|l|}{Accuracy of the computations: $\|(A^TA)_{\theta = 2}{'}-(R^TR)_{\theta = 2}{'}\|=2.17.10^{-14}$}\\  
  \hline
  \end{tabular}
\caption{Illustrative calculation for Example1}
\label{tab:dif_irm_tep}
\end{table}\newpage

相关内容