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A new proof of the elliptical range theorem. (arXiv:1807.04268v1 [math.RA])
来源于:arXiv
The elliptical range theorem asserts that the field of values (or numerical
range) of a two-by-two matrix with complex entries is an elliptical disk, the
foci of which are the eigenvalues of the given matrix. Many proofs of this
result are available in the literature, but most, with one exception, are
computational and quite involved. In this note, it is shown that the elliptical
range theorem follows from the properties of plane algebraic curves and a
straightforward application of a well-known result due to Kippenhahn. 查看全文>>