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Professional mathematician and scientist


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
Jun
12
comment Hermitian positive semi-definite-Square root
Hint: essentially, two matrices commute iff they have the same eigenvectors. The square root of a matrix commutes w/the original matrix...
Jun
12
comment Dirichlet vs Neumann Boundary Conditions of a PDE?
for the Dirichlet and Neumann boundary conditions $\lambda\ge 0$...
Jun
12
revised Inequalities for Laplacian operator eigenvalues
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Jun
12
revised Inequalities for Laplacian operator eigenvalues
added 32 characters in body
Jun
12
comment Inequality between Neumann and Dirichlet eigenvalues
Thank you for the advice. I just did...
Jun
12
asked Inequalities for Laplacian operator eigenvalues
Jun
12
comment Inequality between Neumann and Dirichlet eigenvalues
Does anybody know about the inequalities in the opposite direction? In particular, are there any results on interlacing/alternating of the Dirichlet and Neumann eigenvalues for Laplace-Beltrami operator?...
May
10
awarded  Yearling
Jun
21
comment Find all functions that are analytic on the closed disk and that satisfy
Sorry, one should apply my argument to $f^2(z)/z$, which is bounded and entire, and therefore, constant by Liouville's or Picard's theorem. Then, since $f(z)$ has no branch cut, the constant must be $0$.
Jun
21
comment Find all functions that are analytic on the closed disk and that satisfy
Well, one can apply it to the function $f(z)/\sqrt(z)$, which is bounded and entire. The singularity at $0$ is removable...
Jun
1
revised geometric multiplicity= algebraic multiplicity for a symmetric matrix
fixed grammar...
Jun
1
comment Eigenvalues of a tridiagonal trigonometric matrix
The answer to this question may be helpful: math.stackexchange.com/questions/392908/…
Jun
1
comment Eigenvalues of a tridiagonal trigonometric matrix
Do you have intuition on why the rest of the coefficients of the polynomials are equal?
May
31
comment My son's Sum of Some is beautiful! But what is the proof or explanation?
You may like the somewhat similar pattern in the following question: math.stackexchange.com/questions/390266/…
May
28
comment Solving equations involving modulo operator
Answers to this question may be useful: math.stackexchange.com/questions/389063/…
May
28
comment On integral of a function over a simplex
There are $n^2$ order parameters/unknowns in the problem. The translation and rotation invariance decreases their number only by order $n^2/2$. So, the problem is still complicated in nD... –
May
27
revised Eigenvalues of a tridiagonal trigonometric matrix
added 184 characters in body
May
24
revised Eigenvalues of a tridiagonal trigonometric matrix
added 6 characters in body; edited tags; edited title