Functions > Vector and Matrix > Matrix Factorization > Example: QR Matrix Factorization
  
Example: QR Matrix Factorization
Use the QR function to perform QR matrix factorization.
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• To avoid logical mismatches when performing boolean comparisons, enable Approximate Equality in the Calculation Options drop-down list.
• The example uses a complex matrix as input, but the function also accepts a real matrix as input.
QR Factorization with Pivoting
1. Define a real matrix M1 of dimensions m x n such that m > n.
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2. Set argument p to control the enabling/disabling of pivoting.
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3. Use the QR function to perform QR matrix factorization of matrix M1.
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The default function QR(M1) is equivalent to QR(M,1).
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4. Show that M1 x P1 = Q1 x R1.
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The relationship is logically true.
5. Use the submatrix function to extract matrix M2, such that m < n, then apply the QR function.
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6. Show that M2 x P2 = Q2 x R2.
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The relationship is logically true.
7. Use the submatrix function to extract matrix M3, such that m = n, then apply the QR function.
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8. Show that M3 x P3 = Q3 x R3.
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The relationship is logically true.
QR Factorization with No Pivoting
1. Disable pivoting then apply the QR function to matrix M1 (m > n).
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2. Show that M1 = Q10 x R10.
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The relationship is logically true.
3. Disable pivoting then apply the QR function to matrix M2 (m < n).
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4. Show that M2 = Q20 x R20.
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The relationship is logically true.
5. Disable pivoting then apply the QR function to matrix M3 (m = n).
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6. Show that M3 = Q30 x R30.
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The relationship is logically true.