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QR Factorization

QR Factorization
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2013-03-19 21:20
FunctionCoordinate GeometryMatrix
In collections Linear Algebra with Applications-Interactive Demonstrations
This example demonstrates QR factorization, decomposing matrix A into an orthogonal matrix Q and an upper triangular matrix R. Using GeoGebra commands like Random and Element, the process is dynamically illustrated. Suitable for linear algebra courses on matrix decomposition.

GeoGebra Commands & Parameters

  1. Random(-5, 5) → A1
  2. Random(-5, 5) → C1
  3. Random(-5, 5) → C2
  4. Random(-5, 5) → C4
  5. Random(-5, 5) → C3
  6. Random(-5, 5) → A4
  7. Random(-5, 5) → A3
  8. Random(-5, 5) → A2
  9. Random(-5, 5) → B4
  10. Random(-5, 5) → B3
  11. Random(-5, 5) → B2
  12. Random(-5, 5) → B1
  13. Element(Transpose[ap_2] * ap_2, 1, 1) → length_2
  14. Element(Transpose[ap_3] * ap_3, 1, 1) → length_3

AI Drawing Prompt Reference

Create a matrix A with four randomly generated elements, then decompose it into an orthogonal matrix Q and an upper triangular matrix R. First, generate four random elements for the rows of matrix A, then calculate the elements of Q and R, and finally show the relationship between matrix A, Q, and R.
The prompt above was compiled from the original drawing commands and is for reference only.