## Question

###### UZxiV Let us define p(u,v) Now, it can be observed that if $1 and VutExxuvvizxxv 82 are any two positive scalars, then p(81U, S2v) p(u,v). Hence , the optimization problem is not affected by multiplication with positive scalars; i.e , it does not change under scaling; and hence has infinitely many solutions. To fix the scaling we further constrain the problem by introducing constraints uTExxu vZxxv =1 This leads to constrained optimization of the following form:maxProblem â‚¬ :subject touTzxxu =

uZxiV Let us define p(u,v) Now, it can be observed that if $1 and VutExxuvvizxxv 82 are any two positive scalars, then p(81U, S2v) p(u,v). Hence , the optimization problem is not affected by multiplication with positive scalars; i.e , it does not change under scaling; and hence has infinitely many solutions. To fix the scaling we further constrain the problem by introducing constraints uTExxu vZxxv =1 This leads to constrained optimization of the following form: max Problem â‚¬ : subject to uTzxxu = 1 vTExxV =] Answer the following question: Use the method of Lagrange multipliers to show that the solutions (x, ^) of Problem â‚¬ can be referred to as the generalized eigenvalues and generalized eigenvectors, respec- tively. uTExxv

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