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 May4 awarded Popular Question Jul11 awarded Yearling Jul11 awarded Nice Question Jun14 comment orthogonal eigenvectors My understanding based on en.wikipedia.org/wiki/Principal_component_analysis is that a singular value decomposition (SVD) of $X$ results in three matrices, where the first of them is composed of the eigenvectors of $X^T X$, and is used for PCA. This matrix is always orthogonal. May13 awarded Caucus Jan7 comment Prove a graph with $2n-2$ edges has two cycles of equal length It might be worth adding that for non connected graph, this proof still holds as there is a connected component with $k$ vertices and $2k-2$ edges, because the ratio edges/vertices of the entire graph is $2n-2/n$ so if we have a connectivity component below this ratio, there must be another above it. Dec9 accepted Is coNP closed under Kleene star? Nov28 awarded Scholar Nov28 accepted Prove a graph with $2n-2$ edges has two cycles of equal length Nov28 awarded Editor Nov28 revised Prove a graph with $2n-2$ edges has two cycles of equal length edited body Nov28 asked Prove a graph with $2n-2$ edges has two cycles of equal length Nov16 asked Is coNP closed under Kleene star? Mar3 awarded Supporter Feb27 comment Is quantum logic producing interesting/different mathematics? @Qiaochu I was under the impression that if you change the laws of logic, a lot of proofs become invalid, and that makes different mathematics. @Jim From the little I know, quantum logic talks about prepositions that neither have true nor false value, which reminds me of the intuitionist approach. Feb26 awarded Student Feb26 asked Is quantum logic producing interesting/different mathematics?