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  • 0 posts edited
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  • 26 votes cast
Feb
1
awarded  Notable Question
Nov
26
comment How can I immeediately see that the $L_2$ norms of $X^T X$ and $X X^T$ are the same for all real matrices $X$?
Your equations are for spectral norm, but my question is about $L_2$ norm (en.wikipedia.org/wiki/Matrix_norm#L2.2C1_norm). $L_2$ norm is not equal to maximum eigenvalue.
Nov
21
comment How can I immeediately see that the $L_2$ norms of $X^T X$ and $X X^T$ are the same for all real matrices $X$?
@EricTowers That link is about spectral norm, but I am asking about L2 norm. Why is it relevant?
Nov
20
comment How can I immeediately see that the $L_2$ norms of $X^T X$ and $X X^T$ are the same for all real matrices $X$?
@EricTowers I see, so the L2 norm of a matrix is equal to the L2 norm of vector of its singular values. And the singular values are the same for the two products as can be shown by replacing X by its SVD in the products.
Nov
20
asked How can I immeediately see that the $L_2$ norms of $X^T X$ and $X X^T$ are the same for all real matrices $X$?
Oct
9
awarded  Popular Question
Jul
29
revised Concentration inequalities for product of gaussians
added 10 characters in body
Jul
29
asked Concentration inequalities for product of gaussians
Jul
23
comment Find a set of linear equations whose solution is the same as the minimum of a given quadratic objective function
@Marconius God, I think you guys are right. It was so simple..
Jul
23
asked Find a set of linear equations whose solution is the same as the minimum of a given quadratic objective function
Jul
11
comment Generating a random matrix with all eigenvalues equal to one
The reason for orthogonal matrices is computational rather than mathematical. It is much easier to compute transpose than inverse.
Jul
11
accepted Generating a random matrix with all eigenvalues equal to one
Jul
10
asked Generating a random matrix with all eigenvalues equal to one
Jan
29
accepted How to obtain $n$ maximally different binary vectors with equal number of zeros and ones?
Jan
7
comment How to obtain $n$ maximally different binary vectors with equal number of zeros and ones?
@JorgeFernández The task is to maximize the difference between vectors, not minimize.
Jan
7
comment How to obtain $n$ maximally different binary vectors with equal number of zeros and ones?
@GerryMyerson Thanks, I added the coding-theory tag.
Jan
7
comment How to obtain $n$ maximally different binary vectors with equal number of zeros and ones?
@JorgeFernández I don't see it. For example let $m=10$ and $n=5$. Then the smallest $k$ is $11$. Then say we pick the first 11 digits in the vector. Then what do we do? If we select vectors which have all their ones inside those first 11 digits, then all of them will be very close together, but I need them to be far apart.
Jan
7
revised How to obtain $n$ maximally different binary vectors with equal number of zeros and ones?
edited tags
Jan
7
awarded  Yearling
Jan
7
asked How to obtain $n$ maximally different binary vectors with equal number of zeros and ones?