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.
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QR Factorization with Pivoting
1. Define a real matrix M1 of dimensions m x n such that m > n.
2. Set argument p to control the enabling/disabling of pivoting.
3. Use the QR function to perform QR matrix factorization of matrix M1.
| | The default function QR(M1) is equivalent to QR(M,1).  |
4. Show that M1 x P1 = Q1 x R1.
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The relationship is logically true. | |
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.
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).
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).
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).
6. Show that M3 = Q30 x R30.
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The relationship is logically true. | |