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Quartic Coincidences and the Singular Value Decomposition
John H. Clifford and Michael Lachance
Vol. 86, No. 5 (December 2013), pp. 340-349
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.5.340
Page Count: 10
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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.
Copyright the Mathematical Association of America 2013