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23m
comment show that $(1 +\sin{A}) + \cos^2{A} = 2(1 + \sin{A})$?
Wrong. Try substituting $A =\pi/2$.
38m
comment Product of any two arbitrary positive definite matrices is positive definite or NOT?
possible duplicate of Positive definiteness of the matrix $A+B$
1h
comment Finding pattern
@Chou But then no answer leaves this property true, since the only primes are $2,3,11$, and they are all divisible by $5$.
7h
comment For what types of differential equations is the Laplace transform most effective?
Linear equations, especially (but not only) with constant coefficients. Laplace transform may be used for other types of equations, but it's less straightforward. See an example of the "easy" case here: math.oregonstate.edu/home/programs/undergrad/…
12h
comment Product of any two arbitrary positive definite matrices is positive definite or NOT?
@Batman Agreed, however see this and this. Bad habit, if you want my opinion :)
21h
comment Eigen value and transpose of the $Matrix$
@user120386 Actually, what is troublesome here: if $P(A)=0$, then it's a multiple of a minimal polynomial (say $Q$), because $\Bbb R[X]$ is a principal ring, and polynomials $P$ such that $P(A)=0$ obviously constitute an ideal. But, given some polynomial $P$ such that $P(A)=0$, you only know that $P$ is a multiple of $Q$.
21h
comment Eigen value and transpose of the $Matrix$
@user120386 Wrong, since $AB=I$ and the characteristic polynomial is thus $(x-1)^n$. You have never proved that $x^2-x$ is the minimal polynomial.
1d
comment Prove that sets don't intersect
@LexPodgorny Maybe you could settle once and for all for what you really want to ask :-) I didn't check everything, but you could use $x-2^{2k+1}$ for a suitable $k$.
1d
comment Prove that sets don't intersect
@LexPodgorny I edited the answer.
1d
comment Prove that sets don't intersect
Think about bit patterns in the binary expansion of numbers.
1d
comment Largest eigenvalues of AA' equals to A'A
Why not use the equality, given an eigenvector $v$ instead of an approximation? And you don't even need $n$: if $AA'v=\lambda v$ then $A'AA'v=\lambda A'V$ thus $A'v$ is an eigenvector of $A'A$ for the same eigenvalue.
1d
comment A math contest question related to Ramsey numbers
You may have a look at this: en.wikipedia.org/wiki/Ramsey_theory Your question really is: given a complete graph with 17 vertices, and given that each edge has a color (among three possible colors), show that there is a monochrome complete subgraph with 3 vertices. You can start with 2 colors and 6 vertices instead of 17, to see how it works.
1d
comment Finding the vector perpendicular to the plane
Consider dot product
1d
comment Does the improper integral $\int_{0}^{\infty}\sin(x^2)\;\mathrm dx$ converge?
en.wikipedia.org/wiki/Fresnel_integral
1d
comment To find analytic function with given condition
@YOGESH Yes. Zeros of analytic functions are isolated. What about $f(z)-1$ ?
2d
comment solving the integral of $e^{x^2}$
See Dawson function and this article, which I found in an answer to this question. Not the same Dawson, by the way.
Apr
19
comment Evaluate $\lim _{x\to \infty }\frac{1}{x}\int _0^x\cos\left(t\right)dt\:$
@Lucas You are using a Taylor expansion around $0$, to "prove" divergence at $\infty$. This is wrong (how can you truncate terms that are unbounded?). The limit is also wrong anyway: when $x\to+\infty$, $x-x^3/6$ does not tend toward $+\infty$, but $-\infty$.
Apr
18
comment Show that this path is differentiable but not rectifiable
Regarding differentiability, the only point that is not obvious is $0$. Here you have to use the definition of a derivative, i.e. prove the limit $(f(h)-f(0))/h$ when $h\to0$ exists. However, by computing $f'(x)$ on an interval containing $0$, you will show that it's not bounded, and that the integral that appears in the expression of arc length is not convergent at $0$.
Apr
16
comment What formula can I use to identify numbers in the pattern 2 7 10 15 18 23
Add $3$ or $5$ to the preceding, alternately. But what is really the question?
Apr
16
comment Radius of convergence of $x/sinh(x)$
Yes, you are right. See here