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 Jun 17 comment Finding the limit of a matrix Use the Jordan canonical from Jun 17 comment Suppose that a $3\times 3$ matrix $M$ has an eigenspace of dimension $3$. Prove that $M$ is a diagonal matrix. @user46080 OK, I've messed up with eigenspace and the space spanned by eigenvectors. And I've updated my answer. If you feel it somehow helpful, you can cancel the downvote. Jun 17 revised Suppose that a $3\times 3$ matrix $M$ has an eigenspace of dimension $3$. Prove that $M$ is a diagonal matrix. deleted 245 characters in body Jun 17 revised Suppose that a $3\times 3$ matrix $M$ has an eigenspace of dimension $3$. Prove that $M$ is a diagonal matrix. deleted 245 characters in body Jun 17 revised Suppose that a $3\times 3$ matrix $M$ has an eigenspace of dimension $3$. Prove that $M$ is a diagonal matrix. Texified the title Jun 17 suggested approved edit on Suppose that a $3\times 3$ matrix $M$ has an eigenspace of dimension $3$. Prove that $M$ is a diagonal matrix. Jun 17 revised Suppose that a $3\times 3$ matrix $M$ has an eigenspace of dimension $3$. Prove that $M$ is a diagonal matrix. added 263 characters in body Jun 17 answered Suppose that a $3\times 3$ matrix $M$ has an eigenspace of dimension $3$. Prove that $M$ is a diagonal matrix. Jun 11 awarded Quorum May 17 awarded Yearling May 6 awarded Caucus Apr 17 comment About the spectral radius of a kind of matrices I am sorry but I have left out a condition: at least one entry of $A$ is negative. Apr 17 revised About the spectral radius of a kind of matrices added 161 characters in body Apr 17 comment Cholesky decomposition Cholesky decomposition implies positive-semidefiniteness. Consider $A=0$ and $B=1$, then the new block matrix is not positive semidefinite. Apr 17 revised Prove or disprove: the spectral radius of a matrix with negative entries and row sums as 1 is larger than 1 added 224 characters in body Apr 17 comment Prove or disprove: the spectral radius of a matrix with negative entries and row sums as 1 is larger than 1 I've updated the question at math.stackexchange.com/q/364427/11014 Apr 17 asked About the spectral radius of a kind of matrices Apr 17 comment Prove or disprove: the spectral radius of a matrix with negative entries and row sums as 1 is larger than 1 Hmm...the problem I've actually met seems to have some implied constraints. Anyway thanks for the answer. Apr 17 accepted Prove or disprove: the spectral radius of a matrix with negative entries and row sums as 1 is larger than 1 Apr 17 asked Prove or disprove: the spectral radius of a matrix with negative entries and row sums as 1 is larger than 1