L1-, L2-, Linfty-Norm Proofs - Please Help!
Homework Statement
Show that ||x||1 < or = n||x||infinity and ||x||2 < or = sqrt(n)*||x||infinity for x exists in the set of all real numbers.
Homework Equations
||x||2 is defined here: http://mathworld.wolfram.com/L2-Norm.html
||x||1 is...
Homework Statement
Compute the condition number of the following matrix:
| 1 1 |
| E -E |
where E<<l [SIZE="1"]infinity norm.
Homework Equations
l [SIZE="1"]infinity norm: ||x||[SIZE="1"]infinity = max |x[SIZE="1"]i| where i goes from 1 to n.
Condition number: K(A) =...
Homework Statement
Show that the following function is contractive on the indicated intervals. Determine the best values of [lamda] in Equation (2).
abs(x)^(2/3) on abs(x) < or = 1/3
Homework Equations
A mapping (or function) F is said to be contractive if there exists a number...
Homework Statement
Identify the formula
x[SIZE="1"]n+1 = -2x[SIZE="1"]n + 3yx[SIZE="1"]n^(2/3)
as the Newton's method for a certain function. Here y is a fixed constant. What is the limit of x[SIZE="1"]n?
Homework Equations
Newton's method?:
x[SIZE="1"]n+1 = x[SIZE="1"]n -...
Homework Statement
Consider an iteration function of the form F(x) = x + f(x)g(x), where f(r) = 0 and f'(r) != 0. Find the precise conditions on the function g so that the method of functional iteration will converge cubically to r if started near r.
Homework Equations
I really don't know...
Homework Statement
Determine directly the LLT-Factorization, in which L is a lower triangular matrix with positive diagonal elements, for the matrix
| 4 1/2 1 |
| 1/2 17/16 1/4 |
| 1 1/4 33/64|Homework Equations
I don't know.The Attempt at a Solution
I don't know...
Homework Statement
The highest achievable resolving power of a microscope is limited only by the wavelength used; that is, the smallest item that can be distinguished has dimensions about equal to the wavelength. Suppose one wishes to "see" inside an atom. Assuming the atom to have a diameter...
Homework Statement
A bullet of mass 39 g travels at 1060 m/s. Although the bullet is clearly too large to be treated as a matter wave, determine what Eq. 38-13 predicts for the de Broglie wavelength of the bullet at that speed?
Homework Equations
de Broglie equation: wavelength = h / p...
I never saw the Planet of the Apes lol. It probably would've helped me out with this problem! Thanks for your help, guys! The answer they're looking for is 744 instead of 1488!
Homework Statement
How much work must be done to increase the speed of an electron from rest to 0.52c?
Homework Equations
I don't know :)
The Attempt at a Solution
I tried E=Ymc^2 where Y = 1/[1-(v/c)^2]^1/2 and got 3.19821x10^-22 J which translates to 1.998x10^-9 MeV, but I don't...
Did I misunderstand the question? Is the spaceship going out and then back to Earth all in 105 years? I thought the question meant that the ship went out for 105 years and the return trip also took 105 years (which is why I multiplied by 2).
Homework Statement
The premise of the Planet of the Apes movies and book is that hibernating astronauts travel far into Earth's future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth's future the...
I am having difficulties with the following problem. I have gotten parts (a) and (b) (my correct answers are shown below), but I cannot figure out how to do part (c). Any help with it would be greatly appreciated. Thanks!
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The charges and coordinates of two charged particles...