Question

If A is an orthogonal matrix, find a QR factorization of A

Polynomial factorization
ANSWERED
asked 2021-05-30
If A is an orthogonal matrix, find a QR factorization of A

Answers (1)

2021-05-31

Calculation:
If a matrix A is an orthogonal matrix,
its column are already orthonormal vectors,
so, we don't need to change them using the Gram-Schmidt process to obtain column for Q.
So, we can take \(A=Q\)
Step 2
now, we can find the matrix R from \(A=QR\) using the fact that if A orthogonal it is invertible.
\(A=QR=AR\)
\(\Rightarrow A^{-1}A=A^{-1}AR=R\)
\(\Rightarrow R=I\)
So, QR factorization for an orthogonal matrix \(A=AI\).

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