Yes, similar matrices have the same eigenvalues.
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.
No, in general they do not. They have the same eigenvalues but not the same eigenvectors.
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.
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.
Yes, similar matrices have the same eigenvalues.
you dont...
i am bulimic and i researched it after i was diagnosed.
There is no curent reasurch for XYY syndrome sorry...
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.
no the earth will not blastNo ther is no scientific reasurch that shows thiswe all will be fine
No, in general they do not. They have the same eigenvalues but not the same eigenvectors.
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.
I think it will be shown in 2010 January (from my own reasurch) im not 100% though : )
Sadly, no. I live in Canada, and I've done some reasurch and you can't. It's really sad.
To my reasurch I spsificly dunno because , well who would ask a dumb question like that? Anyone? No? ok LOSERS!
Carl Sheldon Park has written: 'Real eigenvalues of unsymmetric matrices' -- subject(s): Aeronautics