Please help! How to use the vector z (the component of b orthogonal to ColA) to calculate the distance from b to ColA by using built-in function norm?
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Theory: When the columns of A are linearly independent, a vector p is the orthogonal projection of a vector b∉ Col A onto the Col A if and only if p x = Aˆ , where xˆ is the unique least-squares solution of Ax b = , or equivalently, the unique solution of the normal equations T T AA A x b = . Also, if p is the orthogonal projection of a vector b onto Col A, then there exists a unique vector z, such that, z bp = − and z is orthogonal to Col A