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Each point on rotates into that is each point is an

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Unformatted text preview: es into . That is, each point is an eigenvector of corresponding to eigenvalue (b) Suppose rotates points about some line that passes through the origin in . That line consists of all multiples of some nonzero vector . The points on this line do not move under the action of , then . Thus is and eigenvector of corresponding to eigenvalue . The eigenspace is Span . If rotation happens to be half of a full rotation, that is, through and angle of 180 degrees, let be a plane through the origin that is prependecular to line . Each point in the pl...
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