Functions > Vector and Matrix > Matrix Factorization > Example: LU Matrix Factorization
Example: LU Matrix Factorization
Use the LU function to perform LU matrix factorization.
 To avoid logical mismatches when performing boolean comparisons, enable Approximate Equality in the Calculation Options drop-down list.
LU Factorization of a Real Matrix
1. Define a real matrix M1 of dimensions m x n such that m > n.
2. Use the LU function to perform LU matrix factorization of matrix M1.
3. Show that P1 x M1 = L1 x U1.
 P1 m1 0 L1 m1 1 U1 m1 2 P1 M1 L1 U1 P1 M1 L1 U1
The relationship is logically true.
4. Use function submatrix to extract matrix M2 such that m < n.
 M2 submatrix M1 0 1 0 2 m2 LU M2
5. Show that P2 x M2 = L2 x U2.
 P2 m2 0 L2 m2 1 U2 m2 2 P2 M2 L2 U2
The relationship is logically true.
6. Use function submatrix to extract matrix M3 such that m = n.
 M3 submatrix M1 0 2 0 2 m3 LU M3
7. Show that P3 x M3 = L3 x U3.
 P3 m3 0 L3 m3 1 U3 m3 2 P3 M3 L3 U3
The relationship is logically true.
LU Factorization of a Complex Matrix
1. Define a complex matrix C1 of dimensions m x n such that m > n.
2. Use the LU function to perform LU matrix factorization of matrix C1.
3. Show that P4 x C1 = L4 x U4.
 P4 c1 0 L4 c1 1 U4 c1 2 P4 C1 L4 U4 P4 C1 L4 U4
The relationship is logically true.
4. Use function submatrix to extract matrix C2 such that m < n.
 C2 submatrix C1 0 1 0 2 c2 LU C2 P5 c2 0
5. Show that P5 x C2 = L5 x U5.
 L5 c2 1 U5 c2 2 P5 C2 L5 U5
The relationship is logically true.
6. Use function submatrix to extract matrix C3 such that m = n.
7. Show that P6 x C3 = L6 x U6.
 P6 c3 0 L6 c3 1 U6 c3 2 P6 C3 L6 U6
The relationship is logically true.