Eigenvalues of irreducible matrix.
$begingroup$
$A in M_{3x3}(mathbb{R})$ is irreducible and non-negaive matrix with three eigenvalues $lambda_1 , lambda_2 , lambda_3$. Can it be true :
- $lambda_1 = lambda_2 = lambda_3= varrho (A)$
- $lambda_1 =i lambda_2 =-i lambda_3=3$
- $lambda_1=2 , lambda_2=-2 , lambda_3=1$
- $lambda_1=2 , lambda_2=1 , lambda_3=-1$
I think, that first can't be true, because it comes from Frobenius theorem.But I don't know what about the others. So,
1-No, 2-Yes, 3-No, 4-Yes.
matrices
asked Jan 22 at 23:01
pawelKpawelK
527
$endgroup$
add a comment |
$begingroup$
$A in M_{3x3}(mathbb{R})$ is irreducible and non-negaive matrix with three eigenvalues $lambda_1 , lambda_2 , lambda_3$. Can it be true :
- $lambda_1 = lambda_2 = lambda_3= varrho (A)$
- $lambda_1 =i lambda_2 =-i lambda_3=3$
- $lambda_1=2 , lambda_2=-2 , lambda_3=1$
- $lambda_1=2 , lambda_2=1 , lambda_3=-1$
I think, that first can't be true, because it comes from Frobenius theorem.But I don't know what about the others. So,
1-No, 2-Yes, 3-No, 4-Yes.
matrices
asked Jan 22 at 23:01
pawelKpawelK
527
$endgroup$
1
$begingroup$
$det mathbf{A}=prod_{k=1}^{3} lambda_{k}$
$endgroup$
– dantopa
Jan 22 at 23:15
add a comment |
$begingroup$
$A in M_{3x3}(mathbb{R})$ is irreducible and non-negaive matrix with three eigenvalues $lambda_1 , lambda_2 , lambda_3$. Can it be true :
- $lambda_1 = lambda_2 = lambda_3= varrho (A)$
- $lambda_1 =i lambda_2 =-i lambda_3=3$
- $lambda_1=2 , lambda_2=-2 , lambda_3=1$
- $lambda_1=2 , lambda_2=1 , lambda_3=-1$
I think, that first can't be true, because it comes from Frobenius theorem.But I don't know what about the others. So,
1-No, 2-Yes, 3-No, 4-Yes.
matrices
asked Jan 22 at 23:01
pawelKpawelK
527
$endgroup$
$A in M_{3x3}(mathbb{R})$ is irreducible and non-negaive matrix with three eigenvalues $lambda_1 , lambda_2 , lambda_3$. Can it be true :
- $lambda_1 = lambda_2 = lambda_3= varrho (A)$
- $lambda_1 =i lambda_2 =-i lambda_3=3$
- $lambda_1=2 , lambda_2=-2 , lambda_3=1$
- $lambda_1=2 , lambda_2=1 , lambda_3=-1$
I think, that first can't be true, because it comes from Frobenius theorem.But I don't know what about the others. So,
1-No, 2-Yes, 3-No, 4-Yes.
matrices
matrices
asked Jan 22 at 23:01
pawelKpawelK
527
asked Jan 22 at 23:01
pawelKpawelK
527
edited Jan 22 at 23:15
pawelK
asked Jan 22 at 23:01
pawelKpawelK
527
asked Jan 22 at 23:01
pawelKpawelK
527
asked Jan 22 at 23:01
pawelKpawelK
527
527
1
$begingroup$
$det mathbf{A}=prod_{k=1}^{3} lambda_{k}$
$endgroup$
– dantopa
Jan 22 at 23:15
add a comment |
1
$begingroup$
$det mathbf{A}=prod_{k=1}^{3} lambda_{k}$
$endgroup$
– dantopa
Jan 22 at 23:15
1
1
$begingroup$
$det mathbf{A}=prod_{k=1}^{3} lambda_{k}$
$endgroup$
– dantopa
Jan 22 at 23:15
$begingroup$
$det mathbf{A}=prod_{k=1}^{3} lambda_{k}$
$endgroup$
– dantopa
Jan 22 at 23:15
add a comment |
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1
$begingroup$
$det mathbf{A}=prod_{k=1}^{3} lambda_{k}$
$endgroup$
– dantopa
Jan 22 at 23:15