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Eigenvalues of a Projection Matrix

Easy · Data Science · Quant Trader interview question · linear-algebra, eigenvalues, projection, idempotent

A market maker uses a model that involves projecting high-dimensional data onto a lower-dimensional subspace. This projection is represented by a matrix $P$. You discover that the matrix $P$ is idempotent, meaning $P^2 = P$. What are the possible eigenvalues of $P$?