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Post Closed as "Needs details or clarity" by Federico Poloni, Carlo Beenakker, Max Horn, Joseph Van Name, user44191
Minor Math Jaxing
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Daniele Tampieri
Daniele Tampieri
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Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its spectral radius.

Is $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the spectral radius is defined as $\lambda_z=\max\{|\lambda|: \lambda \ is \ eigenvalue \}$ $$ \lambda_z=\max\{|\lambda|:\text{ $\lambda$ is an eigenvalue of $A(z)$}\}. $$

Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its spectral radius.

Is $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the spectral radius is defined as $\lambda_z=\max\{|\lambda|: \lambda \ is \ eigenvalue \}$

Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its spectral radius.

Is $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the spectral radius is defined as $$ \lambda_z=\max\{|\lambda|:\text{ $\lambda$ is an eigenvalue of $A(z)$}\}. $$

deleted 11 characters in body; edited title
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Iosif Pinelis
Iosif Pinelis
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square matrix depending on complex value: largest eigenvaluespectral radius continous?

Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its largest eigenvaluespectral radius.

Are theIs $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the largest eigenvaluespectral radius is defined as $\lambda_z=\max\{|\lambda|: \lambda \ is \ eigenvalue \}$

square matrix depending on complex value: largest eigenvalue continous?

Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its largest eigenvalue.

Are the $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the largest eigenvalue is defined as $\lambda_z=\max\{|\lambda|: \lambda \ is \ eigenvalue \}$

square matrix depending on complex value: spectral radius continous?

Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its spectral radius.

Is $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the spectral radius is defined as $\lambda_z=\max\{|\lambda|: \lambda \ is \ eigenvalue \}$

added 60 characters in body
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Fynn13
Fynn13
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Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its largest eigenvalue.

Are the $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the largest eigenvalue is defined as $\lambda_z=\max\{|\lambda|: \lambda \ is \ eigenvalue \}$

Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its largest eigenvalue.

Are the $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Let $A(z)$ be a $n\times n$ square matrix depending on the complex value $z$ and $\lambda_z$ is its largest eigenvalue.

Are the $\lambda_z$ continous or is it possible that it can jump? Or maybe someone knows a good example for that?

Comment: $A(z)$ consists of complex functions $a_{ij}(z)$ and the largest eigenvalue is defined as $\lambda_z=\max\{|\lambda|: \lambda \ is \ eigenvalue \}$

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Fynn13
Fynn13
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