# 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} 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit LU Decomposition
 The row pivot information in LU decomposition is in one-dimensional array P.
LU Decomposition
 [1-4] /4 Disp-Num5103050100200
[1]  2018/10/21 03:01   Male / 40 years old level / Self-employed people / Not at All /
Purpose of use
Just wanted to check to see if my results matched what the calculator said.
Comment/Request
Your calculator is wrong. I entered a matrix like this:

[1 2 3]
[4 5 6]
[7 8 9]. And it said that the LU decomposition was this:

L [1 0 0] U=....
[0.14 1 0]
[0.57 0 1]

That by itself is wrong, the correct answer is:

L=[1 0 0] U=..... You should figure out to see what's wrong with your algorithm.
[4 1 0]
[7 2 1]
from Keisan
The result seems to be correct.

L
[1 0 0]
[0.14.. 1 0]
[0.57.. 0.5 1]

U
[7 8 9]
[0 0.85.. 1.71..]
[0 0 5.E-15]

LU =
[7 8 9]
[1 2 3]
[4 5 6]

(Partial pivot with row exchange P_i = [3 1 2])
[2]  2018/10/11 15:57   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
helping with my exam
[3]  2018/07/09 12:51   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Doing my homework for me :(
[4]  2018/04/14 09:03   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
check 3x3 matrix LU decomposition

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