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Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.

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Proving: "The trace of an idempotent matrix equals the rank of the matrix"

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Can a sum of idempotents vanish?

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Formal Notation of Functions

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Is there a name for a relationship like idempotence between two functions?

Does every involution have a fixed point?

Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.

Least squares with an idempotent matrix

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