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The simplest method is to start with any vector V which is not collinear with U1 and define (using the vector product "x"):
U2 = U1 x V
U3 = U1 x U2
Mate
g(x) = -a x^2 + x, 0 < a < 1.
(a) p_n - p_(n+1) = a (p_n)^2 > 0
(b) Using induction, 0< p_n <= 1
(c) Denoting p = lim p_n
one obtains using the continuity of g in
p_(n+1) = g(p_n)
that p=g(p) ==> p=0.
The eigenvalue decomposition for A produces:
A = P^(-1) J P
where J is the so called Jordan form of the matrix (it contains all the eigenvalues on the main diagonal) and P is a nonsingular matrix (its column are the eigenvectors if A is "diagonalizable", in which case J is a diagonal matrix)...
Re: How to determine .......
"there are no integral s that exist for functions that osciallate too much or diverge
at very faster rates.. if u could plot the function using matlab or mathematica or maple, then u could see how fast it diverges. i have read this in "fundamentals of calculus" by...
Re: Euler's identity proof
> if someone manage to prove for e^(ax) = b*f(x)+c*g(x) i would be interested.
You probably mean b=b(a), c=c(a) and f,g depend of x only.
It is not difficult to show that such function of 1 variable (b,c,f,g) do not exist!
Mate.
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