  Let y1, y2, y3, a1, a2, a3 > 0 be such that y1 y2 y3 = a1 a2 a3 and y1 + y2 +
y3 >= a1 + a2 + a3, y1 y2 + y2 y3 + y1 y3 >= a1 a2 + a2 a3 + a1 a3.
  Then the following inequality holds (log y1)^2 + (log y2)^2 + (log y3)^2 >=
(log a1)^2 + (log a2)^2 + (log a3)^2.
  This can also be stated in terms of real positive definite 3x3-matrices P1,
P2: If their determinants are equal det P1 = det P2, then tr P1 >= tr P2 and tr
Cof P1 >= tr Cof P2 implies norm(log P1) >= norm(log P2), where log is the
principal matrix logarithm and norm(P) denotes the Frobenius matrix norm.
Applications in matrix analysis and nonlinear elasticity are indicated.
