In the sense that there isn’t a constructive version that could be used instead of it. The constructive version may have stronger assumptions, but if the assumptions are always true for the application, then the constructive version could replace it.
I am doing my ib math paper and I need a way to generate random prime numbers, ranging from 100 to 1000 digits. I have figured out the prime part: Just generating numbers until I find a prime. To check whether a number is prime or not, I am planning on using the AKS test explained in this video.
I have been researching for some time now but I have not yet found a way to generate such numbers. What I have found is that I need some sort of pseudo-random number generator and a source of true randomness. In addition, all numbers should be equally likely.
I know in terms of maps, the * represents “adjoint”. So for instance given a linear map T: V -> W, then T* : W -> V, this has the property that <v, T*(w)> = <T(v), w>.
But what about for matrices? What does * mean in A* where A is a matrix and what properties does A* have? All I know is that the matrix A is normal if A*A = AA* and that it’s self-adjoint if A = A*. I am a bit confused. I tried looking this up and couldn’t get anything. Is adjoint the same as transpose? (ie. A* = At )?
Thanks in advance!
There is an abandoned laboratory on a tropical island. In this laboratory is a calendar that began six years ago, with certain days circled with a red marker and labelled as “shift”. These circled “shift” days occurred once or twice a year at first, but in the last two years the frequency began to accelerate erratically. Soon there were months with multiple shifts, and shifts that lasted for consecutive days. A year ago, the lab was abandoned, and it was untouched until our main character rediscovers it in the present day.
Trying to find a way to mathematically rationalize an exciting and plot relevant reason for the change in frequency (it’s fiction so we can lax the rules a bit).
Just to throw around ideas to explain the increased to frequency of shifts, maybe prime numbered days of the month, or a reverse nth sequence 1 4 9 16 25, or a reverse fibonacci sequence 34 21 13 8 5 3 2 1 1 0, whereupon hitting 0 the island no longer shifts dinosaurs forward into the present day, but starts shifting the main cast backwards into the cretaceous period.
And to explain the increased duration of the shifts… I have no idea. Maybe the first shift is an hour, the second shift is three, etc until there is a shift that lasts for 24 hours.
Just brainstorming here, I think it’s fun to work out things like this. Everything is malleable and I’m open to what you guys think.