5,972 reputation
22142
bio website fph.altervista.org
location Pisa, Italy
age 31
visits member for 4 years, 11 months
seen 44 mins ago

Numerical linear algebra. Mainly matrix equations and their applications (control theory, applied probability).


Oct
20
comment College - Ecuation to solve in 3 variables (p,q,r) in [1,2]
Wow, that's homework? It looks a lot like an Olympiad-like problem at first sight.
Oct
19
revised Strong Law of Large Numbers for arrays of partly dependent random variables
removing tag numerical analysis -- seems to have nothing to do with it
Oct
19
comment Is the notation ${}^t g$ for the transpose of a linear transformation intended to be suggestive?
(Incidentally, unfortunately one cannot extend these operations to a fully-fledged "transposition algebra" with $T^2=1$, since $A^{1+T}\neq A^{T+1}$, i.e., $A^TA\neq AA^T$.)
Oct
19
comment Is the notation ${}^t g$ for the transpose of a linear transformation intended to be suggestive?
In numerical linear algebra, where transposes normally go on the right, the notation $A^{-T} := (A^{-1})^T = (A^T)^{-1}$ is quite common, and on rare occasions I have seen $A^{2T}$. So there is an analogously suggestive solution even putting transposes on the right.
Oct
18
reviewed Approve suggested edit on Number of divisors of an integer of form 4n+1 and 4n+3
Oct
18
revised A calculus question
retagged, in case it stays open
Oct
16
reviewed Approve suggested edit on Untrustworthy people picking a random number
Oct
14
answered The eigenvectors and eigenvalues of matrix geometric mean
Oct
13
comment How to solve a non-homogeneous quadratic matrix equation?
@RobertBryant Thanks for your consideration, but I encourage you to undelete it, I think it was useful. There is nothing wrong with two answers that give different views and information. People can upvote us both. :p
Oct
13
comment How to solve a non-homogeneous quadratic matrix equation?
@RobertBryant I saw your answer only briefly -- why did you delete it? It looked correct to me, and it added some insight on the origin of the solution which my answer currently lacks.
Oct
13
answered How to solve a non-homogeneous quadratic matrix equation?
Oct
13
comment How to solve a non-homogeneous quadratic matrix equation?
Are you sure about those signs? If $G$ has to be symmetric, then $GHG$ has the same signature as $H$, that is, negative definite, but $GHG=M$ tells you that it needs to be positive definite.
Oct
13
reviewed Approve suggested edit on Prime factors of the members of a certain recurrence
Oct
11
answered Approximating the action of the U(N) exponential map
Oct
10
reviewed Approve suggested edit on origami-folding tag wiki excerpt
Oct
9
revised Computing covariance matrix from patchy data
deleted 7 characters in body
Oct
9
comment Examples of eventual counterexamples
There are lots of answers that basically contain only the name of the result and a link to a paper/webpage; I find them very unhelpful and would like to invite the authors to put at least a quick explanation in the text of their answers. In general, link-only answers are frowned upon on many stack exchange websites.
Oct
9
revised eigenvalue estimate of the adjacency matrix
deleted 5 characters in body
Oct
9
comment eigenvalue estimate of the adjacency matrix
Hmm, right. :) What I wrote applies to a generic nonsymmetric nonnegative matrix. Then, in your case, moreover, the 2-norm bound is even more useless, since the 2-norm is $\lambda_\max$.
Oct
9
answered eigenvalue estimate of the adjacency matrix