11,816 reputation
1826
bio website math.missouri.edu/~stephen
location Columbia, MO
age 51
visits member for 2 years, 9 months
seen Oct 16 at 2:23

To find out about me, go to my website. You will probably find out far more than you want to know.


Oct
5
comment Derivative and Integrals of Matrix functions
All you need is that $A(t)$ and $A'(t)$ commute. I think I remember reading somewhere that it isn't a necessary condition, but I am struggling to find the reference.
Oct
5
comment Norm preserving Matrix properties
It is going to include all permutation matrices as well.
Oct
5
comment Derivative and Integrals of Matrix functions
I don't think anyone knows how to do this in general. It is well known that in general $\frac d{dt} e^{A(t)}$ is not the same as $A'(t) e^{A(t)}$.
Sep
30
awarded  Explainer
Sep
21
answered Law of total probability in continous case
Sep
18
comment Sign of Laguerre root finding iteration
I have no idea why they wrote it so awkwardly.
Sep
18
revised Sign of Laguerre root finding iteration
Defined "argument", and explained poster's characterization, and added link to a web page explaining "argument."
Sep
18
revised Sign of Laguerre root finding iteration
Defined "argument", and explained poster's characterization.
Sep
18
answered Sign of Laguerre root finding iteration
Jul
31
comment If the 2-norm of a matrix is small, the trace of the matrix is also small
By the way, $\text{trace}(A) \le n\|A\|$ is true even if $A$ isn't necessarily symmetric. There is nothing in @mfl proof that requires the matrix be diagonalizable.
Jul
3
revised A moment's question.
-1 -> -
Jul
3
comment A moment's question.
OK. But I still think my solution works.
Jul
3
comment linearize a nonlinear ode
Usually you linearize around a fixed point to the equation. Is this what you want?
Jul
3
comment Alternative definition of Euclidean operator norm
I was going to use that $\|\Sigma\| = \rho(\Sigma)$. But your method works just as well.
Jul
3
answered A moment's question.
Jul
3
comment A moment's question.
I think $G^-$ means $G^{-1}$.
Jul
3
comment How do I construct such a numerical method for solving ODE?
By the way, I did not check if you got the calculations for $A$, $B$ and $C$ correct. But your method is correct, and I do happen to know that the resulting numerical formula does produce the utter nonsense you are observing. For $\lambda$ close to zero, the numerical values should grow something like $3^k$ at the $k$ step, no matter how small you make $h$.
Jul
3
comment How do I construct such a numerical method for solving ODE?
It definitely makes sense to me. Notice that you have a linear recurrence relation, which can be solved analytically en.wikipedia.org/wiki/…. Show that there exist $\lambda < 0$ for which the true solution converges to zero, and the numerical solution diverges horribly. The numerical answers genuinely do not remotely resemble the true answers.
Jul
3
comment Random Rotation of Points using Householder matrices
Also, how do you use Euler rotations if $D \ne 3$?
Jul
3
comment Random Rotation of Points using Householder matrices
What's the question? Do you know how to multiply a Householder matrix and a vector in $O(d)$ time? That I can do. The second part I cannot do, because I don't know what a tree is.