Frobenius norm of Fourier matrix
up vote
0
down vote
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Fourier matrix is given as 
where $omega = e^{-2pi i/N}$
Is there any clever way to calculate Frobenius norm of Fourier matrix? I tried solving it with brute force and got some ugly calculations
linear-algebra matrices matrix-calculus
asked Nov 19 at 18:43
Studying Optimization
626
add a comment |
up vote
0
down vote
favorite
Fourier matrix is given as
where $omega = e^{-2pi i/N}$
Is there any clever way to calculate Frobenius norm of Fourier matrix? I tried solving it with brute force and got some ugly calculations
linear-algebra matrices matrix-calculus
asked Nov 19 at 18:43
Studying Optimization
626
Do you know what’s the formula to compute the Frobenius norm?
– lcv
Nov 19 at 18:55
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
Nov 19 at 18:57
Thank you 😊. So you only need to compute the sum of the absolute values squared of all the entries. Note that each entry has modulus one. Can you take it from here?
– lcv
Nov 19 at 19:00
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
Nov 19 at 19:05
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Fourier matrix is given as
where $omega = e^{-2pi i/N}$
Is there any clever way to calculate Frobenius norm of Fourier matrix? I tried solving it with brute force and got some ugly calculations
linear-algebra matrices matrix-calculus
asked Nov 19 at 18:43
Studying Optimization
626
Fourier matrix is given as
where $omega = e^{-2pi i/N}$
Is there any clever way to calculate Frobenius norm of Fourier matrix? I tried solving it with brute force and got some ugly calculations
linear-algebra matrices matrix-calculus
linear-algebra matrices matrix-calculus
asked Nov 19 at 18:43
Studying Optimization
626
asked Nov 19 at 18:43
Studying Optimization
626
asked Nov 19 at 18:43
Studying Optimization
626
asked Nov 19 at 18:43
Studying Optimization
626
asked Nov 19 at 18:43
Studying Optimization
626
626
Do you know what’s the formula to compute the Frobenius norm?
– lcv
Nov 19 at 18:55
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
Nov 19 at 18:57
Thank you 😊. So you only need to compute the sum of the absolute values squared of all the entries. Note that each entry has modulus one. Can you take it from here?
– lcv
Nov 19 at 19:00
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
Nov 19 at 19:05
add a comment |
Do you know what’s the formula to compute the Frobenius norm?
– lcv
Nov 19 at 18:55
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
Nov 19 at 18:57
Thank you 😊. So you only need to compute the sum of the absolute values squared of all the entries. Note that each entry has modulus one. Can you take it from here?
– lcv
Nov 19 at 19:00
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
Nov 19 at 19:05
Do you know what’s the formula to compute the Frobenius norm?
– lcv
Nov 19 at 18:55
Do you know what’s the formula to compute the Frobenius norm?
– lcv
Nov 19 at 18:55
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
Nov 19 at 18:57
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
Nov 19 at 18:57
Thank you 😊. So you only need to compute the sum of the absolute values squared of all the entries. Note that each entry has modulus one. Can you take it from here?
– lcv
Nov 19 at 19:00
Thank you 😊. So you only need to compute the sum of the absolute values squared of all the entries. Note that each entry has modulus one. Can you take it from here?
– lcv
Nov 19 at 19:00
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
Nov 19 at 19:05
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
Nov 19 at 19:05
add a comment |
1 Answer
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This is a straightforward computation using any reasonable definition of the Frobenius norm. For instance, we have
$$
|W| = sqrt{operatorname{tr}(W^*W)} = sqrt{operatorname{tr}(I)} = sqrt{N}
$$
where $W^*W = I$ since $W$ is a unitary matrix.
answered Nov 19 at 19:02
Omnomnomnom
125k788176
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
This is a straightforward computation using any reasonable definition of the Frobenius norm. For instance, we have
$$
|W| = sqrt{operatorname{tr}(W^*W)} = sqrt{operatorname{tr}(I)} = sqrt{N}
$$
where $W^*W = I$ since $W$ is a unitary matrix.
answered Nov 19 at 19:02
Omnomnomnom
125k788176
add a comment |
up vote
0
down vote
accepted
This is a straightforward computation using any reasonable definition of the Frobenius norm. For instance, we have
$$
|W| = sqrt{operatorname{tr}(W^*W)} = sqrt{operatorname{tr}(I)} = sqrt{N}
$$
where $W^*W = I$ since $W$ is a unitary matrix.
answered Nov 19 at 19:02
Omnomnomnom
125k788176
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
This is a straightforward computation using any reasonable definition of the Frobenius norm. For instance, we have
$$
|W| = sqrt{operatorname{tr}(W^*W)} = sqrt{operatorname{tr}(I)} = sqrt{N}
$$
where $W^*W = I$ since $W$ is a unitary matrix.
answered Nov 19 at 19:02
Omnomnomnom
125k788176
This is a straightforward computation using any reasonable definition of the Frobenius norm. For instance, we have
$$
|W| = sqrt{operatorname{tr}(W^*W)} = sqrt{operatorname{tr}(I)} = sqrt{N}
$$
where $W^*W = I$ since $W$ is a unitary matrix.
answered Nov 19 at 19:02
Omnomnomnom
125k788176
answered Nov 19 at 19:02
Omnomnomnom
125k788176
answered Nov 19 at 19:02
Omnomnomnom
125k788176
answered Nov 19 at 19:02
Omnomnomnom
125k788176
125k788176
add a comment |
add a comment |
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Do you know what’s the formula to compute the Frobenius norm?
– lcv
Nov 19 at 18:55
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
Nov 19 at 18:57
Thank you 😊. So you only need to compute the sum of the absolute values squared of all the entries. Note that each entry has modulus one. Can you take it from here?
– lcv
Nov 19 at 19:00
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
Nov 19 at 19:05