# 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
 [1-10] /12 Disp-Num5103050100200
[1]  2019/03/06 08:46   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Check my own code
[2]  2019/03/01 04:30   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Testing my own algorithm
[3]  2019/02/15 12:53   Male / Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of use
checking work
[4]  2019/02/15 04:13   Male / 20 years old level / High-school/ University/ Grad student / A little /
Comment/Request
I need it to work with a 3x4 matrix
[5]  2019/02/12 19:03   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
quick validation
[6]  2019/02/08 03:41   Female / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
university coursework checking
[7]  2018/12/09 05:16   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Check handwritten work.
[8]  2018/11/14 22:43   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Ensure my hand-written decomposition process was done correctly.
[9]  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])
[10]  2018/10/11 15:57   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
helping with my exam

Thank you for your questionnaire.
Sending completion

To improve this 'LU Decomposition Calculator', please fill in questionnaire.
Male or Female ?
Age

Occupation

Useful?

Purpose of use?
Comment/Request (Click here to report a bug).Bug report (Click here to report questionnaire.）
Calculation bug(Please enter information such as specific input values, calculation result, correct result, and reference materials (URL and documents).)
Text bug(Please enter information such as wrong and correct texts)
Your feedback and comments may be posted as customer voice.