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 Jul2 awarded Curious Oct13 comment Linear Algebra : Eigenvalues and rank 1) Do you know that eigen vectors corresponds to different eigen values are linearly independent? Apr4 awarded Yearling Jun8 awarded Caucus Apr4 awarded Yearling Apr1 awarded Nice Question Mar7 suggested rejected edit on Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow P_{j}P_{i}=0$ Mar6 awarded Benefactor Mar6 comment Prime of the form $4p+1$ May I ask from where this confidence comes from? Mar6 comment Extension and Self Injective Ring Thank you for your explanation. I am not very good at ring and module theory, so please be patient with me. If we take our $M$ to be the $R^n$ the Lazarus theorem says that every maximal linear independent set in $M$ is of sixe $n$. I understand that. But doesn't that we are looking for is maximal linearly independent set that contains $Q$. Is this extra requirement (containing $Q$) does not make any difference at all? Mar6 asked Prime of the form $4p+1$ Mar6 comment Extension and Self Injective Ring My understanding of the theorem of Lazarus that you quoted does not guarantee that we can extend $Q$ to $R^n$. It only says if we start we an $R$-module $M$ all maximal linear independent sets in $M$ has the same cardinality. Do I miss something? Mar2 comment Similarity Transformation Thank you for your answer. I am not an expert in this, so I need some clarification. Could you tell me which one-dimensional subspace of $\mathbb{F}^3$ stabilized by $G$ (or doesn't matter which one-dimensional subspace that we choose?). Why $G$ does not stabilize any $2$-dimensional subspace? Mar2 asked Similarity Transformation Feb29 awarded Promoter Feb26 asked Extension and Self Injective Ring Sep12 asked $Ra=Rb$ if and only if $aR=bR$ Jun8 awarded Nice Answer Apr28 accepted Two different ideals with the same annihilator Apr22 revised Two different ideals with the same annihilator added 68 characters in body