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Which property does the matrix Q have in QR decomposition?

easy📝 Conceptual Q2 of 15
SciPy - Linear Algebra (scipy.linalg)
Which property does the matrix Q have in QR decomposition?
AQ is a diagonal matrix
BQ is an orthogonal matrix
CQ is a lower triangular matrix
DQ is a symmetric matrix
Step-by-Step Solution
Solution:

  1. Step 1: Recall the definition of Q in QR decomposition

    Q is defined as an orthogonal matrix, meaning its columns are orthonormal vectors.

  2. Step 2: Confirm the property of Q

    Orthogonal means Q.T * Q = I, which is a key property in QR decomposition.

  3. Final Answer:

    Q is an orthogonal matrix -> Option B

  4. Quick Check:

    Q matrix property = orthogonal [OK]
Quick Trick: Q in QR is always orthogonal (Q.T * Q = I) [OK]
Common Mistakes:
MISTAKES
  • Mistaking Q for diagonal or symmetric
  • Confusing Q with R matrix properties

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