Recent content by digipony

Then for all eigenvalues... λ=tn f(T)v=f(tn)v , therefore f(B) has eigenvalues f(t1), f(t2),... f(tn)

Then f(T)v=(f0+f1T +f2T2...)v = (f0+f1t1 +f2t2...)v =f(t1)v

So you'd have T2v=t2v ... Tnv=tnv

Homework Statement Define a matrix function f(T) of an nxn matrix T by its Taylor series f(T)=f0 +f1T +f2T2+... Show that if matrix T has the eigenvalues t1,t2...tn, then f(T) has eigenvalues f(t1), f(t2)...f(tn) Homework Equations The Attempt at a Solution I am at a loss of how...

Darn- it made the problem so easy, but I guess that was a sign that I was probably doing something that I should not be doing. Thank you for explaining why I could not shuffle the vectors around. :) I did try an example, however it worked out. But I guess it wasn't that good of an example since...

Homework Statement The Attempt at a Solution I am working a physics problem and want to make sure I'm not making a mistake in the math. Here is my math inquiry: Say you have (a*b)(c*d) where * indicates the dot product, and a,b,c, and d are all vectors. Can you say that (a*b)(c*d) =...

Ok, I will try to prove it without summation notation. Thank you

Homework Statement Prove the relation det(AB)=det(A)det(B)Homework Equations det A = \sum_{k}A_{kq} C_{kq} The Attempt at a Solution Here is what I have done: (detA)(detB)= \sum_{k}A_{kq} C_{kq} \sum_{k}B_{kq} C_{kq} = \sum_{k}(A_{kq}B_{kq}) C_{kq} = \sum_{k}(AB)_{kq} C_{kq} =det(A+B) My...

Does anyone know of any good Physics jokes/comics that would be good for a physics group's tshirts and care to share? It's ok if they have a sexual innuendo, but these are for an University organization, so if it has a dirty overtone, it has to be subtle/decent. (To give you some sense of what...

Thank you! I looked for hours trying to find something that makes sense but nothing clicked until ^ this article.

Homework Statement Calculate the density of states if the radiation oscillators are confined to a square (i.e. in two dimensions).Homework Equations The Attempt at a Solution This was one of the questions for my Modern Physics class, (we recently covered blackbody radiation), although based on...

Just wondering here... What is the difference between impedance and resistance? Is resistance typically used to describe the nature of a circuit element, while impedance is of an entire circuit? I have looked up the definitions for both, and I just don't see the difference between them. Thanks!

Never mind: figured it out. If the curvature of the first lens is greater, then it is converging. If the curvature of the second lens is greater, it is diverging.

Homework Statement General question here: If I have a lens that looks like two concave lenses put together (I believe it is called a Meniscus), how do I conceptually tell whether the lens should be converging or diverging? I think I remember reading something saying that it depends upon which...

Oops-Typing error. Thanks! :)