Sò͘-ha̍k siōng, **hâng-lia̍t** (Hàn-jī: 行列, Eng-gí: matrix) sī chi̍t-kóa iàu-sò͘ cho͘-sêng ê tn̂g-ko-hêng tīn-lia̍t. Sòaⁿ-sèng tāi-sò͘ tiong choan-mn̂g gián-kiù hâng-lia̍t ê hun-chi ha̍k-kho sī hâng-lia̍t-lūn, i sī sòaⁿ-sèng tāi-sò͘ siōng kái tiōng-iàu ê chú-tê chi-it.

Tēng-gī
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Hâng-lia̍t sī chi̍t chióng tn̂g-ko-hêng tīn-lia̍t, tīn-lia̍t lāi-tē ê múi chi̍t ba̍k lóng kiò-chò **iàu-sò͘** (Hàn-jī: 要素, Eng-gí: element, entry), in khó-lêng sī sò͘-jī, hû-hō, sò͘-ha̍k-sek ia̍h sī kî-thaⁿ ê sò͘-ha̍k mi̍h-kiāⁿ. Jî-chhiáⁿ koh ū kúi-nā chióng ūn-soàn ē-tàng ēng. 

Hâng-lia̍t lāi-té hoâiⁿ ê chi̍t pâi iàu-sò͘ kiò-chò **chōa** (Hàn-jī: 逝, Eng-gí: row), chhiòng ê chi̍t pâi iàu-sò͘ kiò-chò **khiā** (Hàn-jī: 徛, Eng-gí: column).
It-poaⁿ lâng leh gián-kiù ê hâng-lia̍t, iàu-sò͘ lóng sī sò͘-jī khah chē. Nā-chún chi̍t ê hâng-liat ê iàu-sò͘ lóng sī {\displaystyle K} ê goân-sò͘, lán tiō kóng che hâng-lia̍t sī "tī thé {\displaystyle K} téng-koân" ·ê. Nā chit ê thé sī si̍t-sò͘, tiō chiâⁿ-chò **si̍t hâng-lia̍t** (實行列); nā sī ho̍k-cha̍p-sò͘, tiō chiâⁿ-chò **ho̍k hâng-lia̍t** (複行列).

### Tōa-sè

Hâng-lia̍t ê **tōa-sè** (Hàn-jī: 大細, Eng-gí: size) tiō sī leh kóng i ū jōa-che chōa kap khiā. Siat-sú chi̍t ê hâng-lia̍t ū {\displaystyle m} chōa, {\displaystyle n} khiā, i ê tōa-sè tiō sī {\displaystyle m\times n}, lán kóng i sī "{\displaystyle m\times n} hâng-lia̍t", che ài ēng Eng-gí tha̍k-chò *m by n*.

Kan-taⁿ ū chi̍t chōa ê hâng-lia̍t kiò-chò chōa-hiòng-liōng; kan-taⁿ ū chi̍t khiā ê hâng-lia̍t kiò-chò khiā-hiòng-liōng; chōa kap khiā pêⁿ-chē ê hâng-lia̍t kiò-chò sù-hong hâng-lia̍t.

Overview of a matrix size| Miâ | Tōa-sè | Lē | Biâu-su̍t |
| --- | --- | --- | --- |
| Chōa-hiòng-liōng | {\displaystyle 1\times n} | {\displaystyle {\begin{pmatrix}3&1&-9\end{pmatrix}}} | Kan-taⁿ ū chi̍t chōa ê hâng-lia̍t, ū-sî tiō the̍h lâi piáu-sī hiòng-liōng |
| Khiā-hiòng-liōng | {\displaystyle n\times 1} | {\displaystyle {\begin{pmatrix}5\\0\\3\end{pmatrix}}} | Kan-taⁿ ū chi̍t khiā ê hâng-lia̍t, ū-sî tiō the̍h lâi piáu-sī hiòng-liōng |
| Square matrix | {\displaystyle n\times n} | {\displaystyle {\begin{pmatrix}2&5&9\\8&-1&0\\6&4&3\end{pmatrix}}} | Chōa kap khiā pêⁿ-chē ê hâng-lia̍t. |

Kì-hō
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Kā iàu-sò͘ lóng siá ·chhut-lâi ê sī, hâng-lia̍t it-poaⁿ sī ēng goe̍h-bâi-tiám ia̍h sī oat-bó͘-tiám pau ·khí-lâi, chhin-chhiūⁿ

{\displaystyle \mathbf {A} ={\begin{bmatrix}a\_{11}&a\_{12}&\cdots &a\_{1n}\\a\_{21}&a\_{22}&\cdots &a\_{2n}\\\vdots &\vdots &\ddots &\vdots \\a\_{m1}&a\_{m2}&\cdots &a\_{mn}\end{bmatrix}}={\begin{pmatrix}a\_{11}&a\_{12}&\cdots &a\_{1n}\\a\_{21}&a\_{22}&\cdots &a\_{2n}\\\vdots &\vdots &\ddots &\vdots \\a\_{m1}&a\_{m2}&\cdots &a\_{mn}\end{pmatrix}}=\left\{a\_{ij}\right\}\_{}.}

Ki-pún ūn-soàn
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Lán ē-sái tùi hâng-lia̍t chìn-hêng kúi-nā chióng ūn-soàn, pau-koat *ka-hoat*, *sûn-liōng-chek*, *choán-tì*, *sêng-hoat*, *chōa-ūn-soàn*, kap *chú-hâng-lia̍t*.

### Ka-hoat

Siông-sè chhiáⁿ khoàⁿ: Hâng-lia̍t ê ka-hoat
{\displaystyle {\begin{pmatrix}3&3&2\\0&2&-4\end{pmatrix}}+{\begin{pmatrix}9&0&6\\7&-5&4\end{pmatrix}}={\begin{pmatrix}3+9&3+0&2+6\\0+7&205&-4+4\end{pmatrix}}={\begin{pmatrix}12&3&8\\7&-3&0\end{pmatrix}}}
### Sûn-liōng-chek

Siông-sè chhiáⁿ khoàⁿ: Sûn-liōng-chek
{\displaystyle 4\cdot {\begin{pmatrix}3&-1&-2\\4&-2&5\end{pmatrix}}={\begin{pmatrix}4\cdot 3&4\cdot (-1)&4\cdot (-2)\\4\cdot 4&4\cdot (-2)&4\cdot 5\end{pmatrix}}={\begin{pmatrix}12&-4&-8\\16&-8&20\end{pmatrix}}}
### Sûn-liōng-chek

Siông-sè chhiáⁿ khoàⁿ: Choán-tì
Chi̍t ê Choán-tì

{\displaystyle {\begin{pmatrix}0&8&2\\1&6&9\end{pmatrix}}^{\mathrm {T} }={\begin{pmatrix}0&1\\6&6\\2&9\end{pmatrix}}}

Hun-kái
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Êng-ióng
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Le̍k-sú
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Chham-khó
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