MathDB
Miklós Schweitzer 1957- Problem 1

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October 16, 2015
college contests

Problem Statement

1. Let CijC_{ij} (i,j=1,2,3i,j=1,2,3) be the coefficients of a real non-involutive orthogonal transformation. Prove that the function w=∑i,j=13cijzizjˉw= \sum_{i,j=1}^{3} c_{ ij}z_{i}\bar{z_{ j}} maps the surface of complex unit sphere ∑i=13ziziˉ=1\sum_{i=1}^{3} z_{i}\bar{z_{i}} = 1 onto a triangle of the w-plane. (F. 3)
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