**Tan-ūi hâng-lia̍t** (Hàn-jī: 單位行列, Eng-gí: identity matrix) {\displaystyle I\_{n}} sī chi̍t chióng {\displaystyle n} kai sù-hong hâng-lia̍t, i ê chú tùi-kak-sòaⁿ ê iàu-sò͘ lóng sī chi̍t, kî-thaⁿ só͘-chāi lóng sī lêng.

Tēng-gī kap kì-hō
-----------------

Tan-ūi hâng-lia̍t it-poaⁿ sī siá chò {\displaystyle I\_{n}}; nā-sī size í-keng hô͘ lâng chai-iáⁿ, ia̍h-sī kóng m̄ chāi mā bô iàu-kín, tiō ē-ēng-tit siá chò {\displaystyle I}. Ū-ê léng-he̍k (pí-lūn-kóng liōng-chú le̍k-ha̍k) ē kā tan-ūi hâng-lia̍t siá-chò {\displaystyle {\boldsymbol {1}}}.

Ēng tùi-kak hâng-lia̍t ê kì-hō lâi siá, tiō sī

{\displaystyle I\_{n}=\operatorname {diag} (1,1,\dots ,1).}
Lán mā ē-sái kóng, tan-ūi hâng-lia̍t ê iàu-sò͘ tiō sī Kronecker delta:

{\displaystyle (I\_{n})\_{ij}=\delta \_{ij}.}
Siá khah kū-thé--leh, tiō sī án-ne:

{\displaystyle I\_{1}={\begin{pmatrix}1\end{pmatrix}},\quad I\_{2}={\begin{pmatrix}1&0\\0&1\end{pmatrix}},\quad I\_{3}={\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}},\quad \dots ,\quad I\_{n}={\begin{pmatrix}1&0&0&\cdots &0\\0&1&0&\cdots &0\\0&0&1&\cdots &0\\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\cdots &1\end{pmatrix}}.}

Sèng-chit
---------

Chún-kóng {\displaystyle A} sī chi̍t ê {\displaystyle m\times n} hâng-lia̍t, hâng-lia̍t ê sêng-hoat chŏaⁿ ū chi̍t ê sèng-chit, tiō sī

{\displaystyle I\_{m}A=AI\_{n}=A.}
Te̍k-pia̍t lâi kóng, tan-ūi hâng-lia̍t sī hâng-lia̍t khoân ê sêng-hoat tan-ūi-goân, mā sī it-poaⁿ sòaⁿ-sèng kûn {\displaystyle {\text{GL}}(n)} ê sêng-hoat tan-ūi-goân.

Tan-ūi hâng-lia̍t ê kò͘-iú-ta̍t lóng sī chi̍t, jīm-hô hiòng-liōng lóng sī tan-ūi hâng-lia̍t ê kò͘-iú hiòng-liōng.

Chham-khó chu-liāu
------------------

1. ↑  Friedberg, S. Insel, A. & Spence, L. (2018). *Linear Algebra* (5th Edition). Pearson. ISBN 978-0134860244. p. 82.

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