Let $X$ vector space over $\mathbb{R}$ with $\dim(X)=3$. and let $T\colon X\to X$ be a nilpotent linear map. How can I show that $X$ must have infinitely many $T$-invariant subspaces if and only if $T\circ T=0$.
How to prove this property for a nilpotent map on a vector space
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linear-algebra
functional-analysis
vector-spaces