Yes, similar matrices have the same eigenvalues.
There is no curent reasurch for XYY syndrome sorry...
i am bulimic and i researched it after i was diagnosed.
Call your matrix A, the eigenvalues are defined as the numbers e for which a nonzero vector v exists such that Av = ev. This is equivalent to requiring (A-eI)v=0 to have a non zero solution v, where I is the identity matrix of the same dimensions as A. A matrix A-eI with this property is called singular and has a zero determinant. The determinant of A-eI is a polynomial in e, which has the eigenvalues of A as roots. Often setting this polynomial to zero and solving for e is the easiest way to compute the eigenvalues of A.
I think it will be shown in 2010 January (from my own reasurch) im not 100% though : )
No, in general they do not. They have the same eigenvalues but not the same eigenvectors.
Sadly, no. I live in Canada, and I've done some reasurch and you can't. It's really sad.
no the earth will not blastNo ther is no scientific reasurch that shows thiswe all will be fine
Yes. Simple example: a=(1 i) (-i 1) The eigenvalues of the Hermitean matrix a are 0 and 2 and the corresponding eigenvectors are (i -1) and (i 1). A Hermitean matrix always has real eigenvalues, but it can have complex eigenvectors.
To my reasurch I spsificly dunno because , well who would ask a dumb question like that? Anyone? No? ok LOSERS!
A Hermitian operator has real eigenvalues and is its own conjugate transpose. They always correspond to real observables.
it only eats about 2 times a week because it lives in the oxygen minimum zone (i'm doing a reasurch paper at my school)
Carl Sheldon Park has written: 'Real eigenvalues of unsymmetric matrices' -- subject(s): Aeronautics
James V. Burke has written: 'Differential properties of eigenvalues' -- subject(s): Accessible book
Eigenvalues and eigenvectors are properties of a mathematical matrix.See related Wikipedia link for more details on what they are and some examples of how to use them for analysis.
R S. Caswell has written: 'A Fortran code for calculation of Eigenvalues and Eigenfunctions in real potential wells'
Gaetano Fichera has written: 'Numerical and quantitative analysis' -- subject(s): Differential equations, Eigenvalues, Numerical solutions
An eigenvector is a vector which, when transformed by a given matrix, is merely multiplied by a scalar constant; its direction isn't changed. An eigenvalue, in this context, is the factor by which the eigenvector is multiplied when transformed.
Norman J. Pullman has written: 'Matrix theory and its applications' -- subject(s): Differential equations, Eigenvalues, Matrices
Kenneth A Rathjen has written: 'Enhancement of the CAVE computer code' -- subject(s): Eigenvalues, Data processing, Aerodynamic heating
Matrices are efficient ways to store and manipulate large amounts of data. Matrices are also useful when doing vector analysis, finding least-squares solutions, and eigenvalues.
Hung Chang has written: 'Using parallel banded linear system solvers in generalized Eigenvalue problems' -- subject(s): Eigenvalues
In linear algebra, there is an operation that you can do to a matrix called a linear transformation that will get you answers called eigenvalues and eigenvectors. They are to complicated to explain in this forum assuming that you haven't studied them yet, but their usefulness is everywhere in science and math, specifically quantum mechanics. By finding the eigenvalues to certain equations, one can come up with the energy levels of hydrogen, or the possible spins of an electron. You really need to be familiar with matrices, algebra, and calculus though before you start dabbling in linear algebra.
Gertrude K. Blanch has written: 'Mathieu's equation for complex parameters' -- subject(s): Eigenvalues, Mathieu functions 'On the computation of Mathieu functions'
Have you ever seen the video of the collapse of the Tacoma Narrows Bridge? The Tacoma Bridge was built in 1940. From the beginning, the bridge would form small waves like the surface of a body of water. This accidental behavior of the bridge brought many people who wanted to drive over this moving bridge. Most people thought that the bridge was safe despite the movement. However, about four months later, the oscillations (waves) became bigger. At one point, one edge of the road was 28 feet higher than the other edge. Finally, this bridge crashed into the water below. One explanation for the crash is that the oscillations of the bridge were caused by the frequency of the wind being too close to the natural frequency of the bridge. The natural frequency of the bridge is the eigenvalue of smallest magnitude of a system that models the bridge. This is why eigenvalues are very important to engineers when they analyze structures. (Differential Equations and Their Applications, , pp. ).Car designers analyze eigenvalues in order to damp out the noise so that the occupants have a quiet ride. Eigenvalue analysis is also used in the design of car stereo systems so that the sounds are directed correctly for the listening pleasure of the passengers and driver. When you see a car that vibrates because of the loud booming music, think of eigenvalues. Eigenvalue analysis can indicate what needs to be changed to reduce the vibration of the car due to the music.Eigenvalues can also be used to test for cracks or deformities in a solid. Can you imagine if every inch of every beam used in construction had to be tested? The problem is not as time consuming when eigenvalues are used. When a beam is struck, its natural frequencies (eigenvalues) can be heard. If the beam "rings," then it is not flawed. A dull sound will result from a flawed beam because the flaw causes the eigenvalues to change. Sensitive machines can be used to "see" and "hear" eigenvalues more precisely.Oil companies frequently use eigenvalue analysis to explore land for oil. Oil, dirt, and other substances all give rise to linear systems which have different eigenvalues, so eigenvalue analysis can give a good indication of where oil reserves are located. Oil companies place probes around a site to pick up the waves that result from a huge truck used to vibrate the ground. The waves are changed as they pass through the different substances in the ground. The analysis of these waves directs the oil companies to possible drilling sites.Eigenvalues are not only used to explain natural occurrences, but also to discover new and better designs for the future. Some of the results are quite surprising. If you were asked to build the strongest column that you could to support the weight of a roof using only a specified amount of material, what shape would that column take? Most of us would build a cylinder like most other columns that we have seen. However, Steve Cox of Rice University and Michael Overton of New York University proved, based on the work of J. Keller and I. Tadjbakhsh, that the column would be stronger if it was largest at the top, middle, and bottom. At the points of the way from either end, the column could be smaller because the column would not naturally buckle there anyway.Does that surprise you? This new design was discovered through the study of the eigenvalues of the system involving the column and the weight from above. Note that this column would not be the strongest design if any significant pressure came from the side, but when a column supports a roof, the vast majority of the pressure comes directly from above.Ready to parlay your knowledge of linear algebra into fame and fortune? Read "The 25,000,000,000 Eigenvector: The Linear Algebra Behind Google". (the seventh link below)