Suppose is a finite dimensional vector space and is a linear operator on . Then which of the following conditions must be true for a subspace to be an invariant subspace under ?
Consider the linear transformations for which , the image of , and , the image of , are unit vectors. Let be a linear transformation of this kind which has the additional property that the area of the parallelogram with vertices , , , and is as big as possible. What are the possible values of the measure of the angle between and for the transformation ?