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seen Aug 31 '12 at 23:18

Sep
16
comment limit inferior and superior for sets vs real numbers
For $B_n={1/n}$, shouldn't the $lim~inf~B_n$ and $lim~sup~B_n$ be $\{ 0 \}$ because $lim sup(1/n)=0$ and $lim inf(1/n)=0$ ?
Sep
16
comment limit inferior and superior for sets vs real numbers
never mind got it. I realize that A_n represents a sequence of sets.
Sep
16
comment limit inferior and superior for sets vs real numbers
very nice examples. I didn't understand the 2) example. How did the lim inf get inside the indicator function? Shouldn't limsup and liminf of an indicator function always be 1 and 0, respectively?
Sep
16
comment limit inferior and superior for sets vs real numbers
this example helps make things much clearer. thanks!
Sep
16
accepted limit inferior and superior for sets vs real numbers
Sep
16
revised limit inferior and superior for sets vs real numbers
added 35 characters in body
Sep
16
revised limit inferior and superior for sets vs real numbers
added 12 characters in body; deleted 8 characters in body; added 16 characters in body; added 22 characters in body
Sep
16
comment limit inferior and superior for sets vs real numbers
edited to add curly braces correctly.
Sep
15
awarded  Editor
Sep
15
comment limit inferior and superior for sets vs real numbers
I have added some examples. Can you please answer that will help clarify.
Sep
15
revised limit inferior and superior for sets vs real numbers
added 178 characters in body
Sep
15
asked limit inferior and superior for sets vs real numbers
Sep
13
awarded  Commentator
Sep
13
comment Pivoting in LU decomposition
To summarize, LU decomposition with pivoting does not require matrix to have positive principal minors, it only requires matrix to be non-singular. So it is more stable. The answers below explain what stability means in greater detail. Thanks everyone.
Sep
13
accepted Pivoting in LU decomposition
Sep
9
comment if eigenvalues are positive, is the matrix positive definite?
@J.M. can you give an example of a positive definite but asymmetric matrix?
Sep
9
asked if eigenvalues are positive, is the matrix positive definite?
Aug
31
asked Pivoting in LU decomposition
Aug
16
comment square root of symmetric matrix and transposition
alex - I don't think Q D^{1/2} Q going to be triangular matrix. take for example A = ((2,-2),(-2,5))
Aug
16
comment square root of symmetric matrix and transposition
another related question - if i now assume matrix is symmetric positive definite, and I have diagonalized the matrix as Q DQ^T, is there a way I can convert this quickly to Cholesky decomposition?