Unformatted text preview: properties. Moreover, r 11 = || v 1| || , r jj = || v j ! ||for j=2. .n, and r ij = u i . v j for i< j . Theorem (QR Factorization Algorithm) Consider an n x n matrix M with linearly independent columns v 1 , v 2 ,.. v n . Then the columns q 1 , q 2 ,.. q n of Q and the columns of R can be computed in the following order First col of R, ±rst column of U Second col of R, second col of U and so on EXAMPLE: Find the QR factorization of the matrix 1 2 1 1 1 1 1 2 1 1 1...
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- Fall '08
- QR factorization, 15 gram, (QR Factorization)