Activity for theabbie‭

Type	On...	Excerpt	Status	Date
Edit	Post #288169	Initial revision	—	over 1 year ago
Question	—	Finding a single row of Matrix after exponentiation Suppose I have a matrix $M$ of $N \times N$ and I only want a single row of this matrix after raising it to power $K$ ie. some row of $M ^ K$. This can be done in $O(N^3 \log K)$ at best (or better using advanced matrix multiplication techniques) if we find the entire matrix. However, I am only in... (more)	—	over 1 year ago
Edit	Post #288168	Initial revision	—	over 1 year ago
Question	—	Closed-form expression for sum of Modulo Arithmetic Progression Is there any closed-form expression or at least an efficient way to calculate this sum? $$ \sum{i=1}^{N} (a \cdot i) \bmod{M} $$ we can assume $N$, $a$, and $M$ are large enough such that simple looping is not feasible and that period of the progression is also large. I am aware of the way t... (more)	—	over 1 year ago
Comment	Post #280910	@JoelReyesNoche‭ Putting b=0 makes it an indeterminate form, so, you need to put limits, on which, you get the exact values. (more)	—	almost 4 years ago
Edit	Post #280910	Initial revision	—	almost 4 years ago
Question	—	Approximation of an elliptic integral I used some nice guesswork to get this formula $$\int0^{\frac{\pi}{2}}\sqrt{a^2\sin^2x+b^2\cos^2x}dx=\frac{ab\pi}{\left(a+b\right)\sin\left(\frac{a\pi}{a+b}\right)}$$ The comparision for some values of a and b are $a=a,b=0, value=a, exact=a$ $a=1,b=5, value=5.236, exact= 5.2525$ $a=b, ... (more)	—	almost 4 years ago
Edit	Post #280704	Initial revision	—	almost 4 years ago
Question	—	Why should a non-commutative operation even be called "multiplication"? As per my knowledge and what was taught in school, >$a\times b$ is $a$ times $b$ or $b$ times $a$ Obviously this is commutative as $a$ times $b$ and $b$ times $a$ are same thing. On the other hand there are multiplications like vector multiplication and matrix multiplication that are not comm... (more)	—	almost 4 years ago