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

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Answered question

2021-05-30

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

Answer & Explanation

doplovif

doplovif

Skilled2021-05-31Added 71 answers

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
A1A=A1AR=R
R=I
So, QR factorization for an orthogonal matrix A=AI.

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