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# 5: Matrix Perturbations

The following question arises frequently in matrix theory: What is the smallest possible perturbation of a matrix that causes it to lose rank? We discuss two cases next, with perturbations measured in the 2-norm, and then discuss the measurement of perturbations in the Frobenius norm. This provides us with a new formulation to the least squares estimation problem in which uncertainty is present in the matrix $$A$$ as well as the vector $$y$$. This is known as total least squares.

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