eigenvectors and values of K-diagonal matrix and its 2Dim analogues
From: Alex (alex-math_at_mail.ru)
Date: 02/11/05
- Next message: Dror Speiser: "Lower bound on Waring's problem?? I got a simple result"
- Previous message: Michael Eckhoff: "Re: How can you use a Stochastic Differential Equation"
- Next in thread: Peter Spellucci: "Re: eigenvectors and values of K-diagonal matrix and its 2Dim analogues"
- Reply: Peter Spellucci: "Re: eigenvectors and values of K-diagonal matrix and its 2Dim analogues"
- Messages sorted by: [ date ] [ thread ]
Date: 11 Feb 05 08:45:09 -0500 (EST)
I wrote:
> Alex <alex-math@mail.ru> writes:
> >What are eigenvectors and values of 3-diagonal matrix ?
> >
> >(a , b, 0 , 0 0 0 0
> > b , a, b , 0 0 0 0
> >0 , b, a , b 0 0 0
> >.................................
> >???
> >
> >
And received kind answer:
> homeworK?
It is not a homework - it is related with some work
in signal processing.
> gregory karney: a collection of matrices for testing computational >
algorithms
> example 7.4
> lambda(k)= a+2*b*cos(k*pi/(n+1))
> x(k)(j) = sqrt(2/(n+1))*sin(k*j*pi/(n+1))
Thank You very much !
But i have a contianuation for this question:
What are eigenvectors and values of K-diagonal matrix
of the same kind ?
For example 5-diagonal:
( a , b_1 , b_2 , 0 0 0 0 0
b_1 , a , b_1 , b_2 0 , 0 0 0
b_2 , b_1 , a , b_1 , b_2 , 0 0 0
0 , b_2 , b_1 , a , b_1 , b_2 0 0
0 , 0 , b_2 , b_1 , a , b_1 , b_2 0 0
........................................................
Matrix is of finite size. (In practice i need sizes from 10*10 to
10^4*10^4).
Please pay attention that:
it is not a ciculant type matrix - it is not of the kind
a , b_1 , b_2 , 0 0 0 b_2 b1
.................................................
*******************************
What can be said about two-dimensional analogue for this
averaging operator ?
(I mean the following:
Let us denote by T the shift operator with the matrix
(0 , 1, 0 , 0 0 0 0
0 , 0, 1 , 0 0 0 0
0 , 0, 0 , 1 0 0 0
.......................
Consider the tensor product of the two vector spaces R^n\otimes R^k
and consider the operator:
a T_1 \otimes T_2 + b Id_1 \otimes T_2 + c T_1^{t} \otimes T_2
+ d T_1 \otimes Id_2 + e Id_1 \otimes Id_2 + d T_1^{t} \otimes Id_2
+ c T_1 \otimes T_2^{t} + b Id_1 \otimes T_2^t + a T_1^{t} \otimes
T_2^t
What can be said about its eigenvec and eigenval ?
And the same about its k-diagonal generalizations ?
- Next message: Dror Speiser: "Lower bound on Waring's problem?? I got a simple result"
- Previous message: Michael Eckhoff: "Re: How can you use a Stochastic Differential Equation"
- Next in thread: Peter Spellucci: "Re: eigenvectors and values of K-diagonal matrix and its 2Dim analogues"
- Reply: Peter Spellucci: "Re: eigenvectors and values of K-diagonal matrix and its 2Dim analogues"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
