Inverse Matrix (n-dimensional)

Calculates the inverse of an n×n matrix using LU decomposition.

\(\normalsize A={\left[\begin{array}\\ a_{\small 11}& a_{\small 12}& \cdots& a_{\small 1j}\\ a_{\small 21}& a_{\small 22}& \cdots& a_{\small 2j}\\ \vdots& \vdots& \ddots& \vdots\\a_{\small i1}& a_{\small i2}& \cdots& a_{\small ij}\\\end{array}\right]}\hspace{20px}A A^{\small -1}=A^{\small -1}A=I\\ \)

_{(Click on each cell in the matrix to enter values)}

Matrix A
{aij}

_i＼^j	1	2	3	4
1
2
3
4

The inverse matrix ^A⁻¹ is obtained from the LU decomposition of matrix A using partial pivoting.

\(\normalsize AA^{\small -1} =LUA^{\small -1}=I\\ A^{\small -1}=U^{\small -1}(L^{\small -1}I)\\\)

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