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Idempotent matrices

Source: IMS 2008

May 10, 2008
inductionLaTeXlinear algebramatrixalgebrapolynomial

Problem Statement

Let A1,A2,…,An A_1,A_2,\dots,A_n be idempotent matrices with real entries. Prove that: \mbox{N}(A_1)\plus{}\mbox{N}(A_2)\plus{}\dots\plus{}\mbox{N}(A_n)\geq \mbox{rank}(I\minus{}A_1A_2\dots A_n) \mbox{N}(A) is \mbox{dim}(\mbox{ker(A)})
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