@DavidWheeler the method I cited from Shilov asked me to permute a set of indices in an order like 123456. This could be permuted into 612345 561234 4561234 345612 234561.
Similarly I can do the reverse, 654321 165432 216543 321654 432165 543216. Let's suppose for each term in the determinant I have $a_{a1}a_{b2}a_{c3}a_{d4}a_{e5}a_{f6}$. For a determinant of order 6, there will be 12 terms each with one of the permutations mentioned above. But the term he asked me to find doesn't fit that model. The terms are "out of order" they do not represent a permutation of 123456
Find the curve $\overrightarrow{\sigma}(t)$ that describes the following curve or trajectory. Make a graph.
$$\{(x, y) \mid 4x^2+y^2=1\}$$
How can I find such a curve??
Let's look at the more general case,
$$\sum_{\gcd (p,q) = d} \frac{1}{p^2q^2}.$$
$\gcd (p,q) = d$ means we have $p = d\cdot a$ and $q = d\cdot b$ with $\gcd(a,b) = 1$, so we obtain
$$\sum_{\gcd(p,q) = d} \frac{1}{p^2q^2} = \sum_{\gcd(a,b) = 1} \frac{1}{(da)^2(db)^2} = \frac{1}{d^4}\sum_{\gcd(a...
I am looking at the following exercise:
Consider the initial value problem
$\left\{\begin{matrix}
x''(t)=x(t)\\
x(0)=a\\
x'(0)=b
\end{matrix}\right.$
Write it as a system of First-Order ODES with suitable initial values and show that Euler method can get unstable for a great step $(h)$.
Tha...
