Jiah (Sòaⁿ-sèng tāi-sò͘)

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佇 (Tī)線性 (sòaⁿ-sèng)代數 (tāi-sò͘)中 (tiong)，一 (chi̍t)个 (ê) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle n} 階 (kai)四方 (sù-hong)行列 (hâng-lia̍t) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \mathbf{A}} 的 (ê)跡 (jiah) (漢字: 跡; 英語: trace) 就 (tiō)是 (sī) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \mathbf{A}} 的主對角線 (chú-tùi-kak-sòaⁿ)要素 (iàu-sò͘)的總和 (chóng-hô)，記號 (kì-hō)是 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \operatorname{tr}(\mathbf{A})} [1][2][3]:34

解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \operatorname{tr}(\mathbf{A}) =\sum^n_{i=1} a_{ii} = a_{11} + a_{22} + \cdots + a_{nn} }

其中 (kî-tiong) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle a_{ij}} 代表 (tāi-piáu)行列第 (tē) 解析失敗 (語法錯誤): {\displaystyle {{ruby|伊|i}}} 徛 (khiā)，地 (tē) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle j} 差 (choa̍h)的要素。

尼 (Lē)[修改]

另 (Lēng) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \mathbf{A}} 是按呢 (án-ne)款 (khoán)的行列:解析失敗 (語法錯誤): {\displaystyle \mathbf{A} = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} = \begin{pmatrix} 8 & 2 & 12 \\ -3 & 4 & -3 \\ 1 & 0 & -1 \end{pmatrix}， } 伊的跡就 (tō)是解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê)：從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \operatorname{tr}(\mathbf{A}) = \sum_{i=1}^{3} a_{ii} = a_{11} + a_{22} + a_{33} = 8 + 4 + (-1) = 11.}

參考 (Chham-khó)資料 (chu-liāu)[修改]

  1. ↑ "Rank， trace， determinant， transpose， and inverse of matrices". fourier.應.hmc.edu. 2020-09-09 khòaⁿ--ê. 
  2. ↑ Weisstein, Eric W. (2003). "Trace (matrix)". CRC Concise Encyclopedia of Mathematics (Second edition of 1999 original pán.). Boca Raton， FL: Chapman & Hall. doi:10.1201/9781420035223. ISBN 1-58488-347-2. MR 1944431. Zbl 1079.00009. 2020-09-09 khòaⁿ--ê. 
  3. ↑ Lipschutz, Seymour; Lipson, Marc (September 2005). Schaum's Outline of Theory and Problems of Linear Algebra. McGraw-Hill. ISBN 9780070605022. 
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