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nomadreid

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- Why does Gram-Schmidt turn a matrix into a unitary one?

I understand the rationale for using the Gram-Schmidt process to find an orthogonal (or orthonormal) basis from a given set of linearly independent vectors (e.g., eigenvectors of a Hermitian matrix). However, the rational for using it on the columns of a matrix in order to get a unitary matrix (for example, if one diagonalizes a matrix and one gets a matrix P in PMP

An intuitive explanation would be super. Thanks.

^{-1}which is not unitary) is not clear. (Simply normalizing the columns doesn't work for all matrices.)An intuitive explanation would be super. Thanks.