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seen Mar 9 at 16:41

Jul
2
awarded  Curious
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13
comment Linear Algebra : Eigenvalues and rank
1) Do you know that eigen vectors corresponds to different eigen values are linearly independent?
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awarded  Yearling
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awarded  Caucus
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awarded  Yearling
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awarded  Nice Question
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suggested suggested edit on Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow P_{j}P_{i}=0$
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awarded  Benefactor
Mar
6
comment Prime of the form $4p+1$
May I ask from where this confidence comes from?
Mar
6
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?
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asked Prime of the form $4p+1$
Mar
6
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?
Mar
2
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?
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asked Similarity Transformation
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awarded  Promoter
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26
asked Extension and Self Injective Ring
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asked $Ra=Rb$ if and only if $aR=bR$
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awarded  Nice Answer
Apr
28
accepted Two different ideals with the same annihilator
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22
revised Two different ideals with the same annihilator
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