Abstract
We study the fields of values W(·) of a nonsingular 2 X 2 complex matrix A and of its polar factors V and P (or Q) with A = VP ( = QV ). If trA = 0, then the geometry of W(A) completely determines that of W(P) and W(V) and conversely. We give explicit algebraic formulas and geometric descriptions of this and the general (trA ≠ 0) case.
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