Frobenius norm of Fourier matrix
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 2 days ago
Studying Optimization
596
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 2 days ago
Studying Optimization
596
Do you know what’s the formula to compute the Frobenius norm?
– lcv
2 days ago
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
2 days ago
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
2 days ago
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
2 days ago
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 2 days ago
Studying Optimization
596
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 2 days ago
Studying Optimization
596
asked 2 days ago
Studying Optimization
596
asked 2 days ago
Studying Optimization
596
asked 2 days ago
Studying Optimization
596
asked 2 days ago
Studying Optimization
596
596
Do you know what’s the formula to compute the Frobenius norm?
– lcv
2 days ago
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
2 days ago
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
2 days ago
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
2 days ago
add a comment |
Do you know what’s the formula to compute the Frobenius norm?
– lcv
2 days ago
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
2 days ago
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
2 days ago
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
2 days ago
Do you know what’s the formula to compute the Frobenius norm?
– lcv
2 days ago
Do you know what’s the formula to compute the Frobenius norm?
– lcv
2 days ago
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
2 days ago
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
2 days ago
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
2 days ago
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
2 days ago
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
2 days ago
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
2 days ago
add a comment |
1 Answer
1
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 2 days ago
Omnomnomnom
124k788176
add a comment |
1 Answer
1
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 2 days ago
Omnomnomnom
124k788176
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 2 days ago
Omnomnomnom
124k788176
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 2 days ago
Omnomnomnom
124k788176
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 2 days ago
Omnomnomnom
124k788176
answered 2 days ago
Omnomnomnom
124k788176
answered 2 days ago
Omnomnomnom
124k788176
answered 2 days ago
Omnomnomnom
124k788176
124k788176
add a comment |
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3005333%2ffrobenius-norm-of-fourier-matrix%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Do you know what’s the formula to compute the Frobenius norm?
– lcv
2 days ago
@lcv, yes I do. You can google it if you want to know
– Studying Optimization
2 days ago
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
2 days ago
@lcv, thanks, what I didnt see is that each entry squared has modulus one
– Studying Optimization
2 days ago