Functions > Vector and Matrix > Matrix Factorization > Example: LU Matrix Factorization
  
Example: LU Matrix Factorization
Use the LU function to perform LU matrix factorization.
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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.
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2. Use the LU function to perform LU matrix factorization of matrix M1.
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3. Show that P1 x M1 = L1 x U1.
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The relationship is logically true.
4. Use function submatrix to extract matrix M2 such that m < n.
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5. Show that P2 x M2 = L2 x U2.
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The relationship is logically true.
6. Use function submatrix to extract matrix M3 such that m = n.
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7. Show that P3 x M3 = L3 x U3.
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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.
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2. Use the LU function to perform LU matrix factorization of matrix C1.
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3. Show that P4 x C1 = L4 x U4.
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The relationship is logically true.
4. Use function submatrix to extract matrix C2 such that m < n.
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5. Show that P5 x C2 = L5 x U5.
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The relationship is logically true.
6. Use function submatrix to extract matrix C3 such that m = n.
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7. Show that P6 x C3 = L6 x U6.
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The relationship is logically true.