# LU Decomposition Calculator

## Decomposing a square matrix into a lower triangular matrix and an upper triangular matrix. Partial pivot with row exchange is selected.

 $\hspace{60} A\hspace{50}=\hspace{50}L\hspace{100} U\\\vspace{5}\\\normal{\left[\begin{array}\vspace{10} a_{\small 11}& a_{\small 12}& \cdots& a_{\small 1n}\\\vspace{10} a_{\small 21}& a_{\small 22}& \cdots& a_{\small 2n}\vspace{20}\\ \vdots& \vdots& \ddots& \vdots\vspace{10}\\a_{\small n1}& a_{\small n2}& \cdots& a_{\small nn}\\\end{array}\right]}={\left[\begin{array}\vspace{10} 1& 0& \cdots& 0\\\vspace{10} l_{\small 21}& 1& \cdots& 0\vspace{20}\\ \vdots& \vdots& \ddots& \vdots\vspace{10}\\l_{\small n1}& l_{\small n2}& \cdots& 1\\\end{array}\right]}{\left[\begin{array}\vspace{10} u_{\small 11}& u_{\small 12}& \cdots& u_{\small 1n}\\\vspace{10} 0& u_{\small 22}& \cdots& u_{\small 2n}\vspace{20}\\ \vdots& \vdots& \ddots& \vdots\vspace{10}\\0&0& \cdots& u_{\small nn}\\\end{array}\right]}\\$
 (enter a data after click each cell in matrix) Matrix A {aij}
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt LU分解
 The row pivot information in LU decomposition is in one-dimensional array P.

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