Ludecomposition Calculator
Free Ludecomposition Calculator for linear algebra. Enter values to get step-by-step solutions with formulas and graphs.
Formula
A = L * U
Where A is the original square matrix, L is a lower triangular matrix with ones on its diagonal, and U is an upper triangular matrix. The diagonal of U contains the pivot elements, and the product of the pivots gives the determinant.
Worked Examples
Example 1: 3x3 LU Decomposition
Problem: Find the LU decomposition of A = [[2, 1, 1], [4, 3, 3], [8, 7, 9]].
Solution: Step 1: U row 1 = [2, 1, 1]\nStep 2: L column 1 = [4/2, 8/2] = [2, 4]\nStep 3: U[1][1] = 3 - 2*1 = 1, U[1][2] = 3 - 2*1 = 1\nStep 4: L[2][1] = (7 - 4*1)/1 = 3\nStep 5: U[2][2] = 9 - 4*1 - 3*1 = 2\nL = [[1,0,0],[2,1,0],[4,3,1]], U = [[2,1,1],[0,1,1],[0,0,2]]
Result: det(A) = 2*1*2 = 4 | L and U verified: L*U = A
Example 2: 2x2 LU Decomposition
Problem: Find the LU decomposition of A = [[3, 4], [6, 5]].
Solution: U[0][0] = 3, U[0][1] = 4\nL[1][0] = 6/3 = 2\nU[1][1] = 5 - 2*4 = -3\nL = [[1, 0], [2, 1]]\nU = [[3, 4], [0, -3]]\nVerify: L*U = [[3,4],[6,5]] = A
Result: det(A) = 3*(-3) = -9 | Decomposition verified
Frequently Asked Questions
How accurate are the results from Ludecomposition Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
Can I use Ludecomposition Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
What formula does Ludecomposition Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.