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5: Matrix Perturbations

  • Page ID
    24261
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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.


    This page titled 5: Matrix Perturbations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Mohammed Dahleh, Munther A. Dahleh, and George Verghese (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.