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Feb
25 |
answered | Can t-test be used for non-inferiority hypothesis testing? |
Feb
11 |
awarded | Teacher |
Feb
11 |
answered | Do you find your students are less competent in basic algebra and arithmetic, and, if so, do you believe that this is due to overuse of calculators at an early level? |
Jan
11 |
comment |
Is the direction of the longest line of a polytope unique?
ok I understand. Thanks |
Jan
11 |
comment |
Is the direction of the longest line of a polytope unique?
I edited the question to fix the terminology. |
Jan
11 |
revised |
Is the direction of the longest line of a polytope unique?
Edited to fix terminology as per comment by Harald |
Jan
9 |
comment |
Is the direction of the longest line of a polytope unique?
The way I have defined u_{max} above - it is a vector. However, all elements of u_{max} have the same value and hence we have a hypercube in p dimensions. X can have positive or negative values. The original context in which the above issue arises would constrain X to have only +1, 0 or -1 values but I did not mention this constraint as I felt that the general problem would have a positive answer. |
Jan
9 |
awarded | Supporter |
Jan
9 |
comment |
Is the direction of the longest line of a polytope unique?
Never mind my comment reg $P_v$. The argument does not work. However, I am confused about why you think a rectangle that is perpendicular to the top and the bottom faces of a cube becomes skinnier as $v$ increases. Such a plane will always have the same shape irrespective of the value of $v$. As $v$ increases, the plane shifts towards the origin but retains its orientation. (Note: The longest line is not unique as either diagonal is a longest line but that is a different issue.) |
Jan
8 |
awarded | Student |
Jan
8 |
comment |
Is the direction of the longest line of a polytope unique?
How about this: Define $S$ as the set of points where $L$ intersects the half-planes defined by $u'_i = 0$ and u'_j >= 0 for all $j$ not equal to $i$. I guess we are done if we can show that for some $v > v^*$ all the points in the set $S$ are less than $1$. The above would suggest that $P_v$ lies entirely in the hypercube and hence 'retains' its shape. Does that make sense? ps; I am unable to edit my comments after posting. I hope the above is clear. |
Jan
8 |
comment |
Is the direction of the longest line of a polytope unique?
A clarification: Do you mean the transformation $u'\rightarrow u/v$ instead of $u \rightarrow vu$? |
Jan
8 |
comment |
Is the direction of the longest line of a polytope unique?
@Qiaochu: I am afraid I do not understand your question. My knowledge of math is fairly limited. |
Jan
8 |
awarded | Editor |
Jan
8 |
comment |
Is the direction of the longest line of a polytope unique?
@Deane: Cleaned up notation to indicate that the question relates to real spaces. |
Jan
8 |
revised |
Is the direction of the longest line of a polytope unique?
added 21 characters in body; added 10 characters in body |
Jan
8 |
comment |
Is the direction of the longest line of a polytope unique?
Sorry for the confusion. I do not usually use LaTeX. I cleaned up the LaTeX glitches. |
Jan
8 |
revised |
Is the direction of the longest line of a polytope unique?
deleted 9 characters in body; added 11 characters in body; added 2 characters in body |
Jan
8 |
asked | Is the direction of the longest line of a polytope unique? |