Suppose that K is a nonempty compact convex set in R^n. If f:K->K is not continuous, then f will not have any fixed point.
I believe this statement is false, but I cannot think of a function(not continuous) that maps a compact convex set to another compact convex set.
any tips would be...
Hi I just need some help on understanding some general notation in this quesiton:
Prove if {x_1,x_2,..,x_m} is linearly independent then so is {x_1,x_2,...,x_i-1, x_i+1,...,x_m} for every i in {1,2,...,m}.
I don't really understand what the difference between {x_1,x_2,...,x_i-1...
How is this line wrong ??
A=[[0,1,1][1,0,1][1,1,0]]
xI=[[x,0,0][0,x,0][0,0,x]]
so xI-A=[[x-0,1,1][1,x-0,1][1,1,x-0]]
=[[x,1,1][1,x,1][1,1,x]]
I'm pretty sure this looks ok
Thanks for any help in advance
Find the characteristic and minimal polynomials of
A=[[0,1,1][1,0,1][1,1,0]] (3x3 matrix)
So when I work out my characteristic polynomial I went
det(xI-A)= det[[x,1,1][1,x,1][1,1,x]]
= x(x^2-1)-1(x-1)+1(1-x)
= x^3-3x+2
= (x+2)(x-1)^2
It's...
Hi, I'm having a bit of trouble with this question.
Use the property |integral over c of f(z)dz|<=ML
to show |integral over c of 1/(z^2-i) dz|<=3pi/4
where c is the circle |z|=3 traversed once counterclockwise
thanks in advance for any tips.
ok i finished that part of the question.( this is a 4 part question)
I can't figure out these 2 parts. Any tips would be fantastic
f(x)=x^2*sin(1/x)
1.let g(x)=2x^2 +f(x) (f from the first question i asked)
Show g has a global minimum at x=0 but g'(x) changes sign infinitely...
yeh i got that to work, now how do I show that it's not a local min,max or inflection. Would I look at the second derivative? If that's not defined it's not anything?
let f(x)=sin(1/x)*x^2 for x not 0, and f(0)=0. show that x=0 is a critical point for f which is neither a local minimum, a local maximum, nor an inflection point.
well I tried differentiating this, and got f'=-cos(1/x) +2xsin(1/x). to find a critical point i make f'=0. Not sure how to do...
I think you're right. The wording of the question is not very good. A strict local minimizer is in fact the same as a strict local minimum.
I geuss I'll have to ask the prof
If A is a bounded subset of the reals, show that the points infA, supA belong to the closure A*.
At first the answer seems obvious to me since A* contains its limit points. I'm just having trouble putting it into words, any suggestions would be great, thanks.
The minimizer is the point t where the minimum is. THat's why I'm a bit confused with the question. The wording I was given in my book is a bit awkward.
I think what it means is. For every f(x1,x2) given that x1 and x2 are lines.
There is a minimum at t=0
Those that make sense?
I'm stuck on this question
Show that f(x1,x2) has a strict local minimizer at t=0 along every line
{ x1=at
{ x2=bt
through (0,0).
Any hints or tips would be great thanks