This is probably a silly question but I am not from a maths background. I am a bit confused about betti numbers. From what i know :
The zeroth betti number is the number of connected components in space
The first betti number is the number of loops in space
the second is the number of...
Hello, I am currently looking for a book on functional analysis. However most books I have seen assume knowledge real and complex analysis.
But I am looking for a more superficial introduction covering the important results, some examples of applications (mainly to computational problems)...
I am trying to create the following Matrix without the use of a for loop.
1 2 1 0 0 0 0 0 0 0 0 0
0 0 1 2 1 0 0 0 0 0 0 0
0 0 0 0 1 2 1 0 0 0 0 0
0 0 0 0 0 0 1 2 1 0 0 0
Etc.
Is there a simple way of doing this
Edit: Using Matlab
Well I could use AM-GM , or the method by langrange multiplier but I am interested in how to apply the principle of induction itself when such a condition is given, or if its possible at all .
Homework Statement
If x_{1} x_{2} \cdots x_{n}=1 (1)
show that
x_{1}+x_{2}+\cdots+x_{n} \geq n (2)The Attempt at a Solution
I attempted as follows. I started with
x_{1} + \frac{1}{x_{1}} \geq 2 , which is an inequality I already know how to prove.
Then using Eq.(1) I get
x_{1} +...
There goes 1 hour trying to prove something which is easily disproved. It was one exercise in a Real analysis book. Well atleast I learned how to be critical of everything now ^^
I have been trying the proof of the reverse triangle inequality for n+1 real numbers:
|x-y1-y2-y3-...-yn| \geq | |x| - |y1| - |y2| - |y3| - ...-|yn| |
I know the proof of the reverse triangle inequality for 2 real numbers and the triangle inequality for n numbers. can somebody help ?