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Give an example of nonunitary representation of $mathbb{Z}$
1
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Give an example of nonunitary complex representation of $mathbb{Z}$.
Could anyone give me a hint for solving this problem ?
representation-theory
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
$endgroup$
add a comment |
1
$begingroup$
Give an example of nonunitary complex representation of $mathbb{Z}$.
Could anyone give me a hint for solving this problem ?
representation-theory
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
$endgroup$
$begingroup$
What is a unitary representation?
$endgroup$
– Chris Custer
Feb 1 at 2:14
$begingroup$
A matrix representation of $Bbb Z$ has the form $nmapsto A^n$ where $A$ is a nonsingular matrix. Not all nonsingular matrices are unitary; indeed not all nonsingular matrices are similar to unitary matrices.
$endgroup$
– Lord Shark the Unknown
Feb 1 at 2:17
$begingroup$
Ok. I also looked it up, and apparently $e^{ik}$ might be unitary. What if we put $rneq1$ in front? Does this have any chance?
$endgroup$
– Chris Custer
Feb 1 at 2:31
1
$begingroup$
The representation $T:Bbb{Z} to operatorname{GL}(2,Bbb{C}), z mapsto begin{bmatrix}1 & 0\z & 1end{bmatrix}$ is nonunitary.
$endgroup$
– greelious
Feb 1 at 3:33
add a comment |
1
1
1
$begingroup$
Give an example of nonunitary complex representation of $mathbb{Z}$.
Could anyone give me a hint for solving this problem ?
representation-theory
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
$endgroup$
Give an example of nonunitary complex representation of $mathbb{Z}$.
Could anyone give me a hint for solving this problem ?
representation-theory
representation-theory
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
asked Feb 1 at 2:10
IntuitionIntuition
1,117926
1,117926
$begingroup$
What is a unitary representation?
$endgroup$
– Chris Custer
Feb 1 at 2:14
$begingroup$
A matrix representation of $Bbb Z$ has the form $nmapsto A^n$ where $A$ is a nonsingular matrix. Not all nonsingular matrices are unitary; indeed not all nonsingular matrices are similar to unitary matrices.
$endgroup$
– Lord Shark the Unknown
Feb 1 at 2:17
$begingroup$
Ok. I also looked it up, and apparently $e^{ik}$ might be unitary. What if we put $rneq1$ in front? Does this have any chance?
$endgroup$
– Chris Custer
Feb 1 at 2:31
1
$begingroup$
The representation $T:Bbb{Z} to operatorname{GL}(2,Bbb{C}), z mapsto begin{bmatrix}1 & 0\z & 1end{bmatrix}$ is nonunitary.
$endgroup$
– greelious
Feb 1 at 3:33
add a comment |
$begingroup$
What is a unitary representation?
$endgroup$
– Chris Custer
Feb 1 at 2:14
$begingroup$
A matrix representation of $Bbb Z$ has the form $nmapsto A^n$ where $A$ is a nonsingular matrix. Not all nonsingular matrices are unitary; indeed not all nonsingular matrices are similar to unitary matrices.
$endgroup$
– Lord Shark the Unknown
Feb 1 at 2:17
$begingroup$
Ok. I also looked it up, and apparently $e^{ik}$ might be unitary. What if we put $rneq1$ in front? Does this have any chance?
$endgroup$
– Chris Custer
Feb 1 at 2:31
1
$begingroup$
The representation $T:Bbb{Z} to operatorname{GL}(2,Bbb{C}), z mapsto begin{bmatrix}1 & 0\z & 1end{bmatrix}$ is nonunitary.
$endgroup$
– greelious
Feb 1 at 3:33
$begingroup$
What is a unitary representation?
$endgroup$
– Chris Custer
Feb 1 at 2:14
$begingroup$
What is a unitary representation?
$endgroup$
– Chris Custer
Feb 1 at 2:14
$begingroup$
A matrix representation of $Bbb Z$ has the form $nmapsto A^n$ where $A$ is a nonsingular matrix. Not all nonsingular matrices are unitary; indeed not all nonsingular matrices are similar to unitary matrices.
$endgroup$
– Lord Shark the Unknown
Feb 1 at 2:17
$begingroup$
A matrix representation of $Bbb Z$ has the form $nmapsto A^n$ where $A$ is a nonsingular matrix. Not all nonsingular matrices are unitary; indeed not all nonsingular matrices are similar to unitary matrices.
$endgroup$
– Lord Shark the Unknown
Feb 1 at 2:17
$begingroup$
Ok. I also looked it up, and apparently $e^{ik}$ might be unitary. What if we put $rneq1$ in front? Does this have any chance?
$endgroup$
– Chris Custer
Feb 1 at 2:31
$begingroup$
Ok. I also looked it up, and apparently $e^{ik}$ might be unitary. What if we put $rneq1$ in front? Does this have any chance?
$endgroup$
– Chris Custer
Feb 1 at 2:31
1
1
$begingroup$
The representation $T:Bbb{Z} to operatorname{GL}(2,Bbb{C}), z mapsto begin{bmatrix}1 & 0\z & 1end{bmatrix}$ is nonunitary.
$endgroup$
– greelious
Feb 1 at 3:33
$begingroup$
The representation $T:Bbb{Z} to operatorname{GL}(2,Bbb{C}), z mapsto begin{bmatrix}1 & 0\z & 1end{bmatrix}$ is nonunitary.
$endgroup$
– greelious
Feb 1 at 3:33
add a comment |
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$begingroup$
What is a unitary representation?
$endgroup$
– Chris Custer
Feb 1 at 2:14
$begingroup$
A matrix representation of $Bbb Z$ has the form $nmapsto A^n$ where $A$ is a nonsingular matrix. Not all nonsingular matrices are unitary; indeed not all nonsingular matrices are similar to unitary matrices.
$endgroup$
– Lord Shark the Unknown
Feb 1 at 2:17
$begingroup$
Ok. I also looked it up, and apparently $e^{ik}$ might be unitary. What if we put $rneq1$ in front? Does this have any chance?
$endgroup$
– Chris Custer
Feb 1 at 2:31
1
$begingroup$
The representation $T:Bbb{Z} to operatorname{GL}(2,Bbb{C}), z mapsto begin{bmatrix}1 & 0\z & 1end{bmatrix}$ is nonunitary.
$endgroup$
– greelious
Feb 1 at 3:33