atvirkštinė matrica

atvirkštnė mãtrica, kvadratinė matrica A^–1, kurios sandauga su matrica A lygi vienetinei matricai. Matricos, kurių determinantas lygus nuliui, atvirkštinės matricos neturi. Jei $A=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}{a}_{1l}\\ \mathrm{...}\end{array}\\ a_{k1}\end{array}\\ \mathrm{...}\\ a_{n1}\end{array}\begin{array}{c}\begin{array}{c}\begin{array}{c}\mathrm{...}\\ \mathrm{...}\end{array}\\ \mathrm{...}\end{array}\\ \mathrm{...}\\ \mathrm{...}\end{array}\begin{array}{c}\begin{array}{c}\begin{array}{c}{a}_{1j}\\ \mathrm{...}\end{array}\\ a_{\mathit{kj}}\end{array}\\ \mathrm{...}\\ a_{\mathit{nj}}\end{array}\begin{array}{c}\begin{array}{c}\begin{array}{c}\mathrm{...}\\ \mathrm{...}\end{array}\\ \mathrm{...}\end{array}\\ \mathrm{...}\\ \mathrm{...}\end{array}\begin{array}{c}\begin{array}{c}\begin{array}{c}{a}_{1n}\\ \mathrm{...}\end{array}\\ a_{\mathit{kn}}\end{array}\\ \mathrm{...}\\ a_{\mathit{nn}}\end{array}\right)$ ir jos determinantas |A| ≠ 0, tai \( A^{-1} = \begin{pmatrix} \frac{A_{1l}}{\left | A \right |} & \cdots & \frac{A_{k1}}{\left | A \right |} & \cdots & \frac{A_{n1}}{\left | A \right |} \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ \frac{A_{1j}}{\left | A \right |} & \cdots & \frac{A_{kj}}{\left | A \right |} & \cdots & \frac{A_{nj}}{\left | A \right |} \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ \frac{A_{1n}}{\left | A \right |} & \cdots & \frac{A_{kn}}{\left | A \right |} & \cdots & \frac{A_{nn}}{\left | A \right |} \end{pmatrix} \); čia A_kj yra matricos A elemento a_kj adjunktas. Atvirkštinė matrica naudojama tiesinių lygčių sistemoms spręsti.