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3. In your words, explain what is a nonlinear space. Are the following sets linear or nonlinear: . The unit hypersphere S-{x E Rn+1 llall = 1). . The Stiefel manifold, Sn,-w є RnxdlUTU la} . The set of rotation matrices SO(2)-(O E R2x2 母 ·The set of all n × n matrices. ·The set of all n × n non-singular matrices. 4. Write a matlab program to estimate the quantity: 0o 0 using a Monte Carlo approach. Show the plot of convergence to the limiting value.

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