Trace Norm / Nuclear Norm: How to verify? The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How is the nuclear norm convex whereas the weighted nuclear norm is not?How close is Cartesian product of unit orthogonal bases of SVD to identity matrix?How to define the nuclear norm of a tensor?Variational characterization of nuclear normDistributive property on trace normInequality of square root inside trace normShow that $mathbfX_tr leq sqrtnm f(mathbfX)$computing dual matrix trace norm and tensor gradient in pythonDerivative of the nuclear norm $left$ with respect to $X$Additivity of nuclear norm for projections
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Trace Norm / Nuclear Norm: How to verify?
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How is the nuclear norm convex whereas the weighted nuclear norm is not?How close is Cartesian product of unit orthogonal bases of SVD to identity matrix?How to define the nuclear norm of a tensor?Variational characterization of nuclear normDistributive property on trace normInequality of square root inside trace normShow that $mathbfX_tr leq sqrtnm f(mathbfX)$computing dual matrix trace norm and tensor gradient in pythonDerivative of the nuclear norm $_*$ with respect to $X$Additivity of nuclear norm for projections
$begingroup$
The nuclear norm is defined by this [from wikipedia]:
$$|A|_* = texttrace(sqrtA^*A) = sum_i=i^minm,nsigma_i(A)$$
I get the derivation of this equation. However, I wanted to test it in MATLAB. So used this script:
clc;
clear;
close all;
P = rand([3,4]);
PTP = P'*P;
%compute trace(P'*P)
B = sqrt(P'*P);
S1 = trace(B)
%Compute sum of sigma_i(P)
E = svd(P);
S2 = sum(E)
%Do the same for eigenvalues
E3 = sqrt(eig(P*P'));
S3 = sum(E3)
But for some reason, the values inside S1 and S2 does not match. I do not understand where I did wrong. Could anybody help?
linear-algebra norm svd
edited Apr 9 at 7:32
mathreadler
15.5k72263
asked Apr 8 at 5:57
ponirponir
528
$endgroup$
add a comment |
$begingroup$
The nuclear norm is defined by this [from wikipedia]:
$$|A|_* = texttrace(sqrtA^*A) = sum_i=i^minm,nsigma_i(A)$$
I get the derivation of this equation. However, I wanted to test it in MATLAB. So used this script:
clc;
clear;
close all;
P = rand([3,4]);
PTP = P'*P;
%compute trace(P'*P)
B = sqrt(P'*P);
S1 = trace(B)
%Compute sum of sigma_i(P)
E = svd(P);
S2 = sum(E)
%Do the same for eigenvalues
E3 = sqrt(eig(P*P'));
S3 = sum(E3)
But for some reason, the values inside S1 and S2 does not match. I do not understand where I did wrong. Could anybody help?
linear-algebra norm svd
edited Apr 9 at 7:32
mathreadler
15.5k72263
asked Apr 8 at 5:57
ponirponir
528
$endgroup$
$begingroup$
Welcome to the site by the way. It can be good to learn mathjax typesetting for this site. I helped you turn the wikipedia equation into mathjax code. I think there is a tutorial somewhere. math.meta.stackexchange.com/questions/5020/…
$endgroup$
– mathreadler
Apr 9 at 7:34
add a comment |
$begingroup$
The nuclear norm is defined by this [from wikipedia]:
$$|A|_* = texttrace(sqrtA^*A) = sum_i=i^minm,nsigma_i(A)$$
I get the derivation of this equation. However, I wanted to test it in MATLAB. So used this script:
clc;
clear;
close all;
P = rand([3,4]);
PTP = P'*P;
%compute trace(P'*P)
B = sqrt(P'*P);
S1 = trace(B)
%Compute sum of sigma_i(P)
E = svd(P);
S2 = sum(E)
%Do the same for eigenvalues
E3 = sqrt(eig(P*P'));
S3 = sum(E3)
But for some reason, the values inside S1 and S2 does not match. I do not understand where I did wrong. Could anybody help?
linear-algebra norm svd
edited Apr 9 at 7:32
mathreadler
15.5k72263
asked Apr 8 at 5:57
ponirponir
528
$endgroup$
The nuclear norm is defined by this [from wikipedia]:
$$|A|_* = texttrace(sqrtA^*A) = sum_i=i^minm,nsigma_i(A)$$
I get the derivation of this equation. However, I wanted to test it in MATLAB. So used this script:
clc;
clear;
close all;
P = rand([3,4]);
PTP = P'*P;
%compute trace(P'*P)
B = sqrt(P'*P);
S1 = trace(B)
%Compute sum of sigma_i(P)
E = svd(P);
S2 = sum(E)
%Do the same for eigenvalues
E3 = sqrt(eig(P*P'));
S3 = sum(E3)
But for some reason, the values inside S1 and S2 does not match. I do not understand where I did wrong. Could anybody help?
linear-algebra norm svd
linear-algebra norm svd
edited Apr 9 at 7:32
mathreadler
15.5k72263
asked Apr 8 at 5:57
ponirponir
528
edited Apr 9 at 7:32
mathreadler
15.5k72263
asked Apr 8 at 5:57
ponirponir
528
edited Apr 9 at 7:32
mathreadler
15.5k72263
edited Apr 9 at 7:32
mathreadler
15.5k72263
edited Apr 9 at 7:32
mathreadler
15.5k72263
15.5k72263
asked Apr 8 at 5:57
ponirponir
528
asked Apr 8 at 5:57
ponirponir
528
asked Apr 8 at 5:57
ponirponir
528
528
$begingroup$
Welcome to the site by the way. It can be good to learn mathjax typesetting for this site. I helped you turn the wikipedia equation into mathjax code. I think there is a tutorial somewhere. math.meta.stackexchange.com/questions/5020/…
$endgroup$
– mathreadler
Apr 9 at 7:34
add a comment |
$begingroup$
Welcome to the site by the way. It can be good to learn mathjax typesetting for this site. I helped you turn the wikipedia equation into mathjax code. I think there is a tutorial somewhere. math.meta.stackexchange.com/questions/5020/…
$endgroup$
– mathreadler
Apr 9 at 7:34
$begingroup$
Welcome to the site by the way. It can be good to learn mathjax typesetting for this site. I helped you turn the wikipedia equation into mathjax code. I think there is a tutorial somewhere. math.meta.stackexchange.com/questions/5020/…
$endgroup$
– mathreadler
Apr 9 at 7:34
$begingroup$
Welcome to the site by the way. It can be good to learn mathjax typesetting for this site. I helped you turn the wikipedia equation into mathjax code. I think there is a tutorial somewhere. math.meta.stackexchange.com/questions/5020/…
$endgroup$
– mathreadler
Apr 9 at 7:34
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
On the line
B = sqrt(P'*P);
"sqrt" in Matlab calculates element-wise square root.
You probably want to use "sqrtm" : matrix square root instead.
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
$endgroup$
$begingroup$
That solves the problem! I forgot that it does element wise square root! :(
$endgroup$
– ponir
Apr 9 at 0:22
$begingroup$
@ponir It is good because it meant you did not misunderstand something. It is same with other matrix functions in Matlab, they end with letter "m", for example expm for matrix exponential function. If you are happy with answer please press accept answer button. :)
$endgroup$
– mathreadler
Apr 9 at 7:30
add a comment |
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1 Answer
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oldest
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1 Answer
1
active
oldest
votes
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oldest
votes
active
oldest
votes
$begingroup$
On the line
B = sqrt(P'*P);
"sqrt" in Matlab calculates element-wise square root.
You probably want to use "sqrtm" : matrix square root instead.
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
$endgroup$
$begingroup$
That solves the problem! I forgot that it does element wise square root! :(
$endgroup$
– ponir
Apr 9 at 0:22
$begingroup$
@ponir It is good because it meant you did not misunderstand something. It is same with other matrix functions in Matlab, they end with letter "m", for example expm for matrix exponential function. If you are happy with answer please press accept answer button. :)
$endgroup$
– mathreadler
Apr 9 at 7:30
add a comment |
$begingroup$
On the line
B = sqrt(P'*P);
"sqrt" in Matlab calculates element-wise square root.
You probably want to use "sqrtm" : matrix square root instead.
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
$endgroup$
$begingroup$
That solves the problem! I forgot that it does element wise square root! :(
$endgroup$
– ponir
Apr 9 at 0:22
$begingroup$
@ponir It is good because it meant you did not misunderstand something. It is same with other matrix functions in Matlab, they end with letter "m", for example expm for matrix exponential function. If you are happy with answer please press accept answer button. :)
$endgroup$
– mathreadler
Apr 9 at 7:30
add a comment |
$begingroup$
On the line
B = sqrt(P'*P);
"sqrt" in Matlab calculates element-wise square root.
You probably want to use "sqrtm" : matrix square root instead.
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
$endgroup$
On the line
B = sqrt(P'*P);
"sqrt" in Matlab calculates element-wise square root.
You probably want to use "sqrtm" : matrix square root instead.
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
answered Apr 8 at 6:06
mathreadlermathreadler
15.5k72263
15.5k72263
$begingroup$
That solves the problem! I forgot that it does element wise square root! :(
$endgroup$
– ponir
Apr 9 at 0:22
$begingroup$
@ponir It is good because it meant you did not misunderstand something. It is same with other matrix functions in Matlab, they end with letter "m", for example expm for matrix exponential function. If you are happy with answer please press accept answer button. :)
$endgroup$
– mathreadler
Apr 9 at 7:30
add a comment |
$begingroup$
That solves the problem! I forgot that it does element wise square root! :(
$endgroup$
– ponir
Apr 9 at 0:22
$begingroup$
@ponir It is good because it meant you did not misunderstand something. It is same with other matrix functions in Matlab, they end with letter "m", for example expm for matrix exponential function. If you are happy with answer please press accept answer button. :)
$endgroup$
– mathreadler
Apr 9 at 7:30
$begingroup$
That solves the problem! I forgot that it does element wise square root! :(
$endgroup$
– ponir
Apr 9 at 0:22
$begingroup$
That solves the problem! I forgot that it does element wise square root! :(
$endgroup$
– ponir
Apr 9 at 0:22
$begingroup$
@ponir It is good because it meant you did not misunderstand something. It is same with other matrix functions in Matlab, they end with letter "m", for example expm for matrix exponential function. If you are happy with answer please press accept answer button. :)
$endgroup$
– mathreadler
Apr 9 at 7:30
$begingroup$
@ponir It is good because it meant you did not misunderstand something. It is same with other matrix functions in Matlab, they end with letter "m", for example expm for matrix exponential function. If you are happy with answer please press accept answer button. :)
$endgroup$
– mathreadler
Apr 9 at 7:30
add a comment |
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$begingroup$
Welcome to the site by the way. It can be good to learn mathjax typesetting for this site. I helped you turn the wikipedia equation into mathjax code. I think there is a tutorial somewhere. math.meta.stackexchange.com/questions/5020/…
$endgroup$
– mathreadler
Apr 9 at 7:34