Jiah (Sòaⁿ-sèng tāi-sò͘)

Tī sòaⁿ-sèng tāi-sò͘ tiong, chi̍t ê $n$-kai sù-hong hâng-lia̍t $\mathbf {A}$ ê jiah (Hàn-jī: 跡; Eng-gí: trace) tiō sī $\mathbf {A}$ ê chú-tùi-kak-sòaⁿ iàu-sò͘ ê chóng-hô, kì-hō sī $\operatorname {tr} (\mathbf {A} )$

$\operatorname {tr} (\mathbf {A} )=\sum _{i=1}^{n}a_{ii}=a_{11}+a_{22}+\cdots +a_{nn}$

kî-tiong $a_{ij}$ tāi-piáu hâng-lia̍t tē $i$ khiā, tē $j$ choa̍h ê iàu-sò͘.

Lē

Lēng $\mathbf {A}$ sī án-ne khoán ê hâng-lia̍t:

$$\mathbf {A} ={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{pmatrix}}={\begin{pmatrix}8&2&12\\-3&4&-3\\1&0&-1\end{pmatrix}},$$

i ê jiah tō sī

$$\operatorname {tr} (\mathbf {A} )=\sum _{i=1}^{3}a_{ii}=a_{11}+a_{22}+a_{33}=8+4+(-1)=11.$$