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Exercise 16

Avg difficulty 3.0

A projection is any transformation tt such that t2=tt^{2}=t. (For instance, consider the transformation of the plane R2\mathbb{R}^{2} projecting each vector onto its first coordinate. If we project twice then we get the same result as if we project just once.) What is the minimal polynomial of a projection?

Hefferon, Linear Algebra, Similarity, Polynomials of Maps and Matrices, Exercise 16

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.