Transcription of A Singularly Valuable Decomposition: The SVD of a Matrix
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A Singularly Valuable Decomposition: The SVD of a Matrix
A Singularly Valuable decomposition : The SVD of a MatrixDan KalmanThe American UniversityWashington, DC 20016 February 13, 2002 Every teacher of linear algebra should be familiar with the matrixsingular value decomposition (orSVD). It has interesting and attractive algebraic properties, and conveys important geometrical andtheoretical insights about linear transformations. The close connection between the SVD and the wellknown theory of diagonalization for symmetric matrices makes the topic immediately accessible to linearalgebra teachers, and indeed, a natural extension of what these teachers already know.
Although it is probably not feasible to include the SVD in the flrst linear algebra course, it deflnitely deserves a place in more advanced undergraduate courses, particularly those with a numerical or applied emphasis. My primary goals in this article are to bring the topic to the attention of a broad audience,
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