[Linear Algebra] What does the * mean in terms of matrices?

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!

submitted by Nevin Manimala Nevin Manimala /u/allegiance113
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Need help getting the concept of mean-centering

I was really confused on why the interaction effect changes after centering the variables. The coefficient stays the same, but before centering the variables, let’s say that all the values of the IV was positive. However after centering, some of them become negative. So before centering, all values would have a positive interaction effect while after centering, some values would have a positive interaction effect while some would have a negative. Can anyone please tell me why and if I did something wrong?

submitted by Nevin Manimala Nevin Manimala /u/collegethrowaway717
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Writing a story where dinosaurs begin appearing on an island due to “shifts” that happen sporadically. Trying to find out a way to explain the increasing frequency of these “shifts” mathematically (fibonacci sequence, etc). Brainstorm with me?

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.

submitted by Nevin Manimala Nevin Manimala /u/colkcolkcolk
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Intersection of Geometric Measure Theory and PDE?

Hey guys, I’m currently in a seminar class on topics in geometric measure theory and I’ve been tasked with preparing a talk on recent-ish research (past 15 years or so) on a topic of my choice. My interests lie in PDE (maybe), and I was wondering if anyone had any insights on recent interesting problems in the intersection of GMT and PDE.

Thanks!

submitted by Nevin Manimala Nevin Manimala /u/UnorthodoxGentleman
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