Martin Sleziak
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 17h revised There exists a homomorphism $f : G \to H$ with $|G| = 20$ and $|im f | = 6$ edited body; edited tags 20h revised The shortest distance problem by using Gram-Schmidt Process TeX: \langle, \rangle Apr24 revised How to simplify $\sum_{r=1}^{y} \binom{x-1}{r}\binom{y-1}{r}$? edited tags Apr24 revised Is $\gcd(2^{2n}+1, 3)=1$? added (gcd) tag Apr24 revised $a^2 = 2b^3 = 3c^5$ Find the smallest value of $abc$. edited tags Apr24 comment Extreme points of the unit balls of $l^\infty, C([0,1])$ Apr24 comment Extreme points of the unit balls of $l^\infty, C([0,1])$ Related question to the last part: Extreme points of unit ball of Banach spaces $\ell_1$, $c_0$, $\ell_\infty$ Apr24 revised Extreme points of unit ball of Banach spaces $\ell_1$, $c_0$, $\ell_\infty$ edited title Apr24 answered Getting perpendicular distance by Gram Schmidt Process Apr24 comment Abstract Linear Algebra Inner Product Your question was put on hold, the message above (and possibly comments) should give an explanation why. You might try to edit your question to address these issues. Note that the next edit puts your post in the review queue, where users can vote to reopen this. (Therefore it would be good to avoid minor edits and improve your question as much as possible with the next edit.) Apr24 comment Abstract Linear Algebra Inner Product I've noticed that you have asked three questions during the last 3 hours. I wanted to make sure that you are aware of the quotas 50 questions/30 days and 6 questions/24 hours, so that you can plan posting your questions accordingly. (If you try to post more questions, StackExchange software will not allow you to do so.) For more details see meta. Apr24 revised Getting perpendicular distance by Gram Schmidt Process edited body Apr24 comment How to show $\int_{x_0-\delta}^{x_0+\delta} g(x) > 0$ if $g(x_0)>0$? For some basic information about writing math at this site see e.g. here, here, here and here. Apr24 comment How to show $\int_{x_0-\delta}^{x_0+\delta} g(x) > 0$ if $g(x_0)>0$? A more natural hint would be (in my opinion) to find function $f$ such that $f(x)\le g(x)$ on $[x_0-\delta,x_0+\delta]$. (The post suggest looking for a function where this inequality is fulfilled on the whole interval $[0,1]$.) Apr24 revised How to show $\int_{x_0-\delta}^{x_0+\delta} g(x) > 0$ if $g(x_0)>0$? added 368 characters in body Apr24 revised How to show $\int_{x_0-\delta}^{x_0+\delta} g(x) > 0$ if $g(x_0)>0$? added 168 characters in body; edited tags Apr24 comment How do you diagonalize this matrix and find P and D such that A = PDP^-1? Note that similar matrices have the same trace. Therefore it cannot be A. And you also know that, if there exists a diagonal matrix, then the sum of diagonal elements must be $-11$ and only numbers $-4$ and $-3$ are allowed on diagonal. (In B and C you are given matrices which are not diagonal. So if you know that one of the possibilities A, B, C, D must be correct, only D remains. Given the wording of the question, I would expect also E: There do not exist such P and D.) Apr24 revised Calculate a determinant. edited tags Apr24 revised Abstract Linear Algebra Inner Product added 240 characters in body Apr24 comment Abstract Linear Algebra Inner Product The vectors $\vec v_i$ do not have lenght equal to !, so you need to modify them a bit. Also, you should put these vectors in rows, since you want $\vec u$ to be the first row. Notice that you still will need do some minor changes if one of the vectors $\vec v_1,\dots,\vec v_{n-1}$ is zero, i.e., if the given vector $\vec u$ contains two consecutive zeroes.