Your idea was very useful, but I found an alternative solution (page 18).
The algorithm:
S_0=Q_0
Defactorize: \, A_n=Q_nR_n
A_{n+1}=R_nQ_n
S_{n+1}=S_nQ_n
As the algorithm converges, A_n become a diagonal matrix, whose diagonal elements give the eigenvalues. And the column vectors of S_n gives...
My aim was to numerically calculate eigenvalues and eigenvectors for a square A matrix.
I managed to find the eigenvalues by using QR algorithm. Now, I can find all of the eigenvalues for any given square matrix. But, for the next step, how do I find the corresponding eigenvectors? Is there...
[PLAIN]https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-snc7/313028_10150383340891940_666206939_8328916_99129355_n.jpg
Would this system work, if the air-water isolation problem (water leakage into the air tank) is solved?
If it would work, where does the input energy comes from? We obtain...
I have an A matrix with dimensions 1x1. Its the only term a11 is an arbitrary number.
For what values of a11, this A matrix is;
Diagonal
Upper triangular
Lower triangular
Hmm. I will substitute columns of the identity matrix for b vector for n times to find n different x vectors. Next, I will merge these x vectors to form the inverse of the A matrix. Did I understand it right?
In the Ax=b equation I'm working with, A is a square matrix, x and b are column vectors.
Like this:
So, how do I make the b vector an nxn identity matrix?
Thank you for your guidance. I will stick to LU decomposition.
This is an interesting information.
I didn't understand what b vector to choose for calculating the inverse of A. Can you please a b vector and explain the method to find the inverse of A matrix?
I want to solve the linear equation below:
Ax = b
For this purpose, I'm writing a C++ code. I have written both routines for decomposing A matrix to L and U matrices, and for calculating inverse of A matrix.
I may multiply both sides with A-1:
Ax = b
A^{-1}Ax = A^{-1}b
x =...
There are two points on the 2D rectangular coordinate system, namely P and M.
Their positions are function of time and are:
Position \, of \, P: \, (p_x(t), \, p_y(t))
Position \, of \, M: \, (m_x(t), \, m_y(t))
Distance between them is:
R(t) \, = \, \sqrt{(p_x - m_x)^2 \, + \, (p_y -...
I think the title is self-descriptive. This question stuck in my mind. I want to learn how much energy is stored in human fat.
Does this amount of energy density change in every human?
If so what is the variance of this distribution?
Shortly: How is glass tube produced?
I'm currently working on a project, in which I am planning to use glass tubes of sizes 1.5m length, 1.8mm thickness, 4cm and 5cm outer diameters. It will be cost effective to produce my own glass tubes when I start the mass production of the overall...
One of my friends is insisting that a car can go 19000km with only 1kg of http://en.wikipedia.org/wiki/Borax" , and only one tea-spoon of borax can extract as much energy 100 tons of coal does.
Is that true?
Does borax contain this much of chemical energy?
Could it be by solving it with the equation below?:
x(t) = e^{At}x(t-T) + \int_{t-T}^{t} e^{A(t - \tau)}Bu(\tau)d\tau
"T" is the sampling period of the input signal. To calculate the state vector between any two input samples, I will just solve this equation. Would this method work? Even...