Math Forum / Mathematics / Undergraduate Math / December 2005

Let F be a field, A be a square matrix over F,
and p be an arbitrary polynomial over F.
If x is an eigenvalue of A,
then p(x) is an eigenvalue of p(A).

You have all run across desperate google ads by this guy called Steven Cullinane who claims to have discovered something called "Diamond Theory". He preaches his "advanced mathematics" from multiple domains:
"Plato's diamond throws new light on
finite geometry and combinatorics."

I have three questions that I can't seem to figure out
on my own.
1)
f(x)=log[a](x)

Sometime early in the coming year I'll be introducing 6th graders to a way of organizing polyhedra, one inside the other, plus showing how their volumes might be related.  
I learned this way of doing it from Bucky Fuller, the geodesic dome guy.  I've covered the same or similar ...

I did the case were x is odd, y even, and z is odd.
Case x, y, odd, z even.
3y^2 = z^2 - x^2 = (z + x)(z - x)
So 3 | (z + x) or 3 | (z - x)

Let A be a square block upper-triangular matrix,
in which the diagonal blocks are square matrices
that do not necessarily have the same dimensions,
then the determinant of A equals the product of the determinants of its diagonal blocks.

My boyfriend is doing a sports science course and has devised a questionnaire to measure the impact of video feedback on performance. He has come to me to find a suitable statistical test but as i am only doing A level statistics i only know of those for normally distributed data ...

Hi, I'm having a problem solving the following using the Gauss-Jordan Elimination Method. I am wondering if someone can help me...
2x + 5y - z = -3
x - y + 4z = 20
3x + 2y - z = 3  

Hi. I'm to
       Find all solutions to the equation
               x^2 + 2y^2 = w^2                             (1)
       with x > 0, y > 0, w > 0.

I'm trying to prove the theorem:
For integers x and z, prime p, if (x+z)/p and (x-z)/p are integers,
(x,z) = 1, then (x+z)/p and (x-z)/p are relatively prime.
If p = 2, its very easy. But is there some weird method for p > 2.

(Reposted from wrong area)
This is in regards to an operator on a complex inner product space. This is something I've been wondering about for a while - is it possible to generate a Jordan basis which is orthonormal?
Does it suffice to norm the generalized eigenvectors as we ...

What is some good software that will teach calc 1 and 2?
I am looking for tutorial software and something I can plug in stuff to
check work.
Years ago I bought some stuff called mathmateca,  are they even still

There are functions that at particular points don't have
a derivative. Examples of those function are :f(x)=|x|
doesn't have derivative at point x=0 and f(x)=-|x-4|+5
doesn't have derivative at point x=4.

Last summer i had posted this statement.I still maintain that all values of N ,when not DECIMALIZED , are rational vulgar fractions.

There were four critical media articles about Dave Touretzky on the
net, informing about how the alleged free speech activist David
Touretzky goes after publications that he doesn't like. But they were
removed from the net. Why doesn't he say that the only free speech he