Can someone explain gram schmidt orthogonalisation process?

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Devsi Bantva

Please see book "Elementary Linear Algebra : Application Version by H. Anton and C. Rorres Chapter 6, Page no.323-325. Keep following me. Best Wishes.

Ulrich Mutze

You need to know that the method as it is explained in elementary books is useless in numerical applications. In the famous book by Press et al. 'Numerical Recipes in C' we read (p.66) "Numerically, however, because of the build-up of roundoff errors, naive Gram-Schmidt orthogonalization is t e r r i b l e ." They then describe how singular value decomposition (SVD) can be used to improve things. This improved version often goes under the name of 'principal component analysis'.

Elementary books give original idea about method. However for numerical applications you have to make application of this method.