Problems

4.1 Show that the set of equations

Σθ=p

si322_e

has a unique solution if Σ > 0 and infinite many if Σ is singular.

4.2 Show that the set of equations

Σθ=p

si323_e

always has a solution.

4.3 Show that the shape of the isovalue contours of the mean-square error (J(θ)) surface

J(θ)=J(θ*)+(θθ*)TΣ(θθ*)

si324_e

are ellipses whose axes depend on the eigenstructure of Σ.

Hint

Assume that Σ has discrete eigenvalues.

4.4 Prove that if the true relation between ...

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