Question: 12.11. Let Al ~ A2;;:>: ... ;;:>: Aq be the roots of 1 II - AIzl = 0, where II and 12 are q X

12.11. Let Al ~ A2;;:>: ... ;;:>: Aq be the roots of 1 II - AIzl = 0, where II and 12 are q X q positive definite covariance matrices.

(a) What does Al = Aq = 1 imply about the relationship of II and I2?

(b) What does Aq> 1 imply about the relationships of the ellipsoids x'I;-lx

= c and x'I2'ix = c?

(c) What does Al > 1 and Aq < 1 imply about the relationships of the ellipsoids x'I;-lx=c and x'I2'lx=c?

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