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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
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May
17
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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