Recent content by mathematicsma

Very interesting points. I sometimes wonder about that, too. Who am I? In other words, which part of me is the self and which part is external? Obviously, everything going on inside my brain comes from me, but it often seems that there is some part of the brain that is more central to my...

I know this is an old thread, and this is only a tangential topic, but it's been something I've always wondered about: For those of us who think mostly in words, and have conversations with ourselves, do you refer to yourself as "you" in your thoughts? When I am thinking through an issue...

Thanks. I didn't know about that site, I might actually use it. Does anyone know anything about the differences between the different editions? I have used books (Calculus -Larson, for example) where there are absolutely no changes from one edition to the next other than nicer graphics. Even...

I have a feeling this is the wrong place to post this. I can never figure out where to put things :confused: Anyway, my professor uses the 4th edition of Edwards and Penney Differential Equations and Boundary Value Problems (https://www.amazon.com/gp/product/0131561073/?tag=pfamazon01-20)...

Redbelly: when I first heard the experiment, I immediately thought I should choose zero. Then, like you, I realized that if even one person doesn't think like me, and chooses another number, my results are off. Like you, until I did some research, I never imagined it would be so high. Note that...

I second drankin. Anyway, what is the mind? It's just a word people throw around, so I'm not sure how to characterize it.

Okay, the experiment is over. I thank everyone who participated, you all helped. I ended it about a week ago, but then finals caught up with me, and I didn't have a chance to follow up. So here it is: The official results...

I didn't check all your work, but my initial reaction: all four matrices have to be complex matrices, that's the initial condition. If they're not complex, the conjugate transpose is the same as the transpose, and they're just simple symmetric matrices. Am I wrong?

I just realized something: If AB=(AB)*=B*A*=BA, then AB commutes. But that is only true if A, B, and AB are all Hermitian. Alternatively, we can say that if A, B are both Hermitian and AB commutes, then AB=BA=B*A*=(AB)*, so we know that AB is Hermitian. That's why the property I cited from...

Sorry about forgetting the brackets. I fixed that. Okay, (XY)*=Y*X*. So we can rewrite as AD-(CB)*=I. But how does that help? My main problem is that we don't know that any of the individual matrices A, B, C, D are Hermitian. If we could prove that, we're done. B*C* is the same as BC...

Homework Statement Let A, B, C, D be nxn complex matrices such that AB and CD are Hermitian, i.e., (AB)*=AB and (CD)*=CD. Show that AD-B*C*=I implies that DA-BC=I The symbol * indicates the conjugate transpose of a matrix, i.e., M* is the conjugate transpose of M. I refers to the identity...

Point well taken. You're correct on both counts. I meant fractions that cannot be expressed as integers between 0 and 100.:approve: And I guess if you're around the area between zero and one, then precision starts to matter.

Interesting thought. Oh well, there's no prize. Other than the ability to pat yourself on the back and convince yourself you're a genius. Then, since you're so darn good at anticipating the behavior of others, become a day trader on the stock markets, or trade currency options, or something...

Fractions are legitimate. But it strikes me as remarkable that people are that confident in their choices that they need such precision. I think most people think about whether it'll be in the range of, say, 15, or in the area of 35. Not whether it'll be 15 or 15.375. If there some kind...

Yes, but there may be a self-selecting group of people that announce their answers. I'm not sure they're representative of the rest of us.:smile: I also assumed that we were supposed to choose an integer between 0 and 100, inclusive. Turns out I didn't specify it in the instructions, so I...