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Quartic Coincidences and the Singular Value Decomposition

John H. Clifford and Michael Lachance
Mathematics Magazine
Vol. 86, No. 5 (December 2013), pp. 340-349
DOI: 10.4169/math.mag.86.5.340
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.5.340
Page Count: 10
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Quartic Coincidences and the Singular Value Decomposition
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Abstract

Summary The singular value decomposition is a workhorse in many areas of applied mathematics and the insights it gives to linear transformations is beautiful. Using the geometry given by the SVD, we prove that the critical points of a quartic polynomial whose zeros are the vertices of a parallelogram are the foci and center of an inscribed ellipse passing through the midpoints of the sides of the parallelogram.

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