矩阵概论
为了模拟情况,矩阵是表示和操作数据的有用方法。矩阵中的元素可以表示数据、方程或系统,并在现实生活中有许多应用。
什么是矩阵?
- 矩阵是A矩形阵列的元素(数值的或代数的)排列在行而且列
- 的订单矩阵的数量它的行和列
- 矩阵的阶
" class="Wirisformula" role="math" alt="米" style="vertical-align:-6px;height:22px;width:16px">行和m {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="n" style="vertical-align:-6px;height:22px;width:11px">列n {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="M叉乘n" style="vertical-align:-6px;height:22px;width:43px">m × n {"language":"en","fontFamily":"Times New Roman","fontSize":"18"}
- 矩阵的阶
- 一个矩阵
" class="Wirisformula" role="math" alt="粗体斜体A" style="vertical-align:-6px;height:22px;width:16px">可以定义为A {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="粗体斜体A等于左括号A下标ij结束下标右括号" style="vertical-align:-12px;height:28px;width:63px">在哪里A = ( a i j ) {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="I = 1,空格2,空格3,空格…逗号空格m" style="vertical-align:-6px;height:22px;width:117px">而且i = 1 , 2 , 3 , . . . , m {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="J = 1,空格2,空格3,空格…逗号空格n" style="vertical-align:-6px;height:22px;width:112px">而且j = 1 , 2 , 3 , . . . , n {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="一个下标ij结束下标" style="vertical-align:-12px;height:28px;width:19px">指向行中的元素a i j {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="我" style="vertical-align:-6px;height:22px;width:7px">、列i {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="j" style="vertical-align:-6px;height:22px;width:7px">j {"language":"en","fontFamily":"Times New Roman","fontSize":"18"}
有什么类型的矩阵?
- 一个列矩阵(或列向量)是一个矩阵单独的列,
" class="Wirisformula" role="math" alt="N = 1" style="vertical-align:-6px;height:22px;width:37px">n = 1 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} - 一个行矩阵矩阵有a吗单行,
" class="Wirisformula" role="math" alt="M = 1" style="vertical-align:-6px;height:22px;width:42px">m = 1 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} - 一个方阵其中的行数是平等的对列数,
" class="Wirisformula" role="math" alt="M = n" style="vertical-align:-6px;height:22px;width:43px">m = n {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} - 两个矩阵是平等的当他们是相同的顺序和他们的对应的元素是平等的,即
" class="Wirisformula" role="math" alt="A下标ij下标等于b下标ij下标" style="vertical-align:-12px;height:28px;width:55px">对于所有元素a i j = b i j {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} - 一个零矩阵,
" class="Wirisformula" role="math" alt="粗体斜体O" style="vertical-align:-6px;height:22px;width:16px">,是一个矩阵,其中所有的元素都是O {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="0" style="vertical-align:-6px;height:22px;width:10px">,如。0 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="粗体斜体O等于开括号表0行0结束表0行0" style="vertical-align:-21px;height:54px;width:81px">O = 0 0 0 0 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} - 单位矩阵,
" class="Wirisformula" role="math" alt="加粗斜体I" style="vertical-align:-6px;height:22px;width:9px">,是一个广场矩阵中的所有元素沿主对角线是I {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="1" style="vertical-align:-6px;height:22px;width:10px">剩下的是1 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="0" style="vertical-align:-6px;height:22px;width:10px">,如。0 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="粗体斜体I等于开括号表第1行0结束表第0行1闭括号" style="vertical-align:-21px;height:54px;width:74px">I = 1 0 0 1 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"}
考试技巧
- 确保你知道如何在GDC中输入和存储矩阵
工作的例子
让矩阵
一)
写下的顺序A {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="粗体斜体A" style="vertical-align:-6px;height:22px;width:16px" loading="lazy">.
b)
说明a 2 , 3 {"language":"en","fontFamily":"Times New Roman","fontSize":"18"} " class="Wirisformula" role="math" alt="A下标2,3结束下标" style="vertical-align:-12px;height:28px;width:28px" loading="lazy">.