How to find a formula for the eigenvalues of a tridiagonal matrix
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I have the following tridiagonal matrix,
$$ T = begin{pmatrix}
frac{1}{2}alpha & beta & 0 & cdots & 0 \
beta & alpha & beta & cdots & 0 \
vdots & ddots & ddots & ddots & vdots \
0 & 0 & beta & alpha & beta\
0 & 0 & 0 & beta & alpha
end{pmatrix},$$
where $alpha+2beta=1$ and $alpha,beta>0.$ I want to find a closed formula for the eigenvalues and eigenvectors. Have anyone any idea?
linear-algebra
asked Nov 16 at 16:29
math_lover
9010
add a comment |
up vote
0
down vote
favorite
I have the following tridiagonal matrix,
$$ T = begin{pmatrix}
frac{1}{2}alpha & beta & 0 & cdots & 0 \
beta & alpha & beta & cdots & 0 \
vdots & ddots & ddots & ddots & vdots \
0 & 0 & beta & alpha & beta\
0 & 0 & 0 & beta & alpha
end{pmatrix},$$
where $alpha+2beta=1$ and $alpha,beta>0.$ I want to find a closed formula for the eigenvalues and eigenvectors. Have anyone any idea?
linear-algebra
asked Nov 16 at 16:29
math_lover
9010
2
What is it in the case of a $3times3$ matrix?
– Matthew Leingang
Nov 16 at 16:31
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have the following tridiagonal matrix,
$$ T = begin{pmatrix}
frac{1}{2}alpha & beta & 0 & cdots & 0 \
beta & alpha & beta & cdots & 0 \
vdots & ddots & ddots & ddots & vdots \
0 & 0 & beta & alpha & beta\
0 & 0 & 0 & beta & alpha
end{pmatrix},$$
where $alpha+2beta=1$ and $alpha,beta>0.$ I want to find a closed formula for the eigenvalues and eigenvectors. Have anyone any idea?
linear-algebra
asked Nov 16 at 16:29
math_lover
9010
I have the following tridiagonal matrix,
$$ T = begin{pmatrix}
frac{1}{2}alpha & beta & 0 & cdots & 0 \
beta & alpha & beta & cdots & 0 \
vdots & ddots & ddots & ddots & vdots \
0 & 0 & beta & alpha & beta\
0 & 0 & 0 & beta & alpha
end{pmatrix},$$
where $alpha+2beta=1$ and $alpha,beta>0.$ I want to find a closed formula for the eigenvalues and eigenvectors. Have anyone any idea?
linear-algebra
linear-algebra
asked Nov 16 at 16:29
math_lover
9010
asked Nov 16 at 16:29
math_lover
9010
edited Nov 16 at 16:31
asked Nov 16 at 16:29
math_lover
9010
asked Nov 16 at 16:29
math_lover
9010
asked Nov 16 at 16:29
math_lover
9010
9010
2
What is it in the case of a $3times3$ matrix?
– Matthew Leingang
Nov 16 at 16:31
add a comment |
2
What is it in the case of a $3times3$ matrix?
– Matthew Leingang
Nov 16 at 16:31
2
2
What is it in the case of a $3times3$ matrix?
– Matthew Leingang
Nov 16 at 16:31
What is it in the case of a $3times3$ matrix?
– Matthew Leingang
Nov 16 at 16:31
add a comment |
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What is it in the case of a $3times3$ matrix?
– Matthew Leingang
Nov 16 at 16:31