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Gram-Schmidt Orthogonalization and QR Decomposition

Gram-Schmidt Orthogonalization and QR Decomposition
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2019-09-30 23:45
This example demonstrates the Gram-Schmidt orthogonalization process to transform a set of vectors into an orthogonal set and shows the QR decomposition. By manipulating the row vectors E, O1 to O4, you can observe the steps of orthogonalization and QR decomposition. This example is suitable for learning linear algebra concepts of vectors and matrices.

GeoGebra Commands & Parameters

  1. List E
  2. List O1
  3. List O2
  4. List O3
  5. Numeric O4(NaN)
  6. List A
  7. List Q
  8. List R
  9. List L

AI Drawing Prompt Reference

Demonstrate the Gram-Schmidt orthogonalization process to transform a set of vectors into an orthogonal set and show QR decomposition. Adjust row vectors E, O1 to O4 to observe the steps of orthogonalization and QR decomposition. Use dashed lines for the initial vector set and solid lines for the orthogonalized set, marking the start and end points of each vector, and showing the orthogonality relationships between them.
The prompt above was compiled from the original drawing commands and is for reference only.