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revised The myth of no prime formula?
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revised The myth of no prime formula?
Tao was misquoted
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awarded  Good Answer
1d
revised The myth of no prime formula?
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awarded  Nice Answer
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revised The myth of no prime formula?
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answered The myth of no prime formula?
Sep
21
awarded  Cleanup
Sep
21
revised determinant in terms of quadratic form evaluated at a point
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Sep
11
comment What explains this bizarre behavior?
@medicu: the comments above by mercio imply that the answer to your last question is yes. I've provided some additional details in my own answer, in case the reasons are not immediately clear.
Sep
11
comment What explains this bizarre behavior?
My previous comments in response to your question were misleading, so I've deleted them, and expanded my answer instead. In particular, there was nothing non-rigourous about the statement that points in $(-0.994334,-0.989663)$ converge to $+\infty$ as I had stated in my comment. (I'd forgotten how I carried out the original calculations back in May 2013.
Sep
11
revised What explains this bizarre behavior?
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Sep
3
comment Linear Algebra - Row Echelon Form vs Reduced Row Echelon Form (Uniqueness)
I'm not seeing how this addresses the original question, which was concerned with the number of nonzero rows in a row echelon matrix. In the context of the OP's question, you need to insist that $L$ be nonsingular. If you do that, then $U$ and $R$ will have the same number of nonzero rows. In other words, the answer to the OP's question (Can different row echelon forms of the same matrix have different numbers of nonzero rows?) is no.
Sep
3
comment Linear Algebra - Row Echelon Form vs Reduced Row Echelon Form (Uniqueness)
Another way to look at it: suppose one row echelon form of a matrix had one nonzero row and another row echelon form of the same matrix had two nonzero rows. The row operations that lead to row echelon form are reversible. So there would be a sequence of row operations that turned the matrix with one nonzero row into the row echelon matrix with two nonzero rows. But the only thing row operations can produce in a matrix with one nonzero row are scalar multiples of the nonzero row. You could therefore never end up with a row echelon matrix with two nonzero rows.
Sep
3
comment Linear Algebra - Row Echelon Form vs Reduced Row Echelon Form (Uniqueness)
The number of nonzero rows in row echelon form must be the same for all different row echelon forms of the same matrix. The number of nonzero rows in a matrix in row echelon form is, in fact, the rank of the matrix. But rank is not changed by row operations.
Sep
3
comment Modular forms are arithmetic objects
I assume you've seen this MathOverflow question?
Aug
24
comment Proof of the inclusion-exclusion formula in probability
Those intersections that contain $A_{n+1}$ in your last expression are of size $k+1,$ not size $k.$ So instead of $(-1)^{k+1}$ you should have $(-1)^{k+2}.$
Aug
24
answered Proof of the inclusion-exclusion formula in probability
Aug
20
revised All permutation matrices that convert one Hadamard matrix into another Hadamard matrix.
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Aug
19
revised Interpretation of partial derivatives of vertical coordinate with respect to $x$ and time
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