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?

1 次查看（过去 30 天）

Tianlan Yang 2021-4-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/796887-please-help-how-to-use-the-vector-z-the-component-of-b-orthogonal-to-cola-to-calculate-the-distan

评论： Tianlan Yang 2021-4-8

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