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Engineering LibreTexts

5: Matrix Perturbations

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  • 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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