Reputation
12,087
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
3 16 41
Newest
 Generalist
Impact
~205k people reached

3h
comment Other solutions to 1+1 = 2
Your binary numbers and roman numbers examples are not actually different from the usual definition of $1$, it's just that the numbers are being written differently.
4h
comment Why is this a bounded operator?
Your work is correct, but the upper bound is too weak. For example, suppose $T = \sum_k e_{k,k}$. Then $T$ is the identity map and hence bounded, but computing $\|T\| \le \sum_k \|e_{k,k}\|$ is far too weak an estimate.
12h
answered Simple question - represent vector with respect to a basis
Jul
20
comment Spectral radius of a real, symmetric, positive semi - definite matrix.
@A.G. What is considered elementary? That the matrix 2-norm and spectral radius are related is already 99% of the way there, basically, as you used in the $i = j$ case.
Jun
22
comment Determining whether x=1 is a regular singular point in the differential equation
I have covered the method in generality. $x_0$ is the placeholder I'm using for whichever point you're trying to check.
Jun
20
answered Determining whether x=1 is a regular singular point in the differential equation
Jun
20
revised Determining whether x=1 is a regular singular point in the differential equation
latex
Jun
20
reviewed Approve Fredholm equation
Jun
19
comment Complex Eigenvalues and systems of 1st-order ODEs
Well, the solutions would have the form $\mathbf{v}(t) = e^{\lambda t} \mathbf{v}_0$, and we have Euler's formula to convert complex exponentials into trig functions...does that sound familiar?
Jun
18
comment How can I use a precise definition to find values of delta that correspond with given epsilon values
@Grace, not equals, but "near". And no, you're not finding a new value of $a$, you're finding the distance $\delta$. So you want to find how close $x$ needs to be to $a = 2$ so that $|x^3 - 3x + 4 - 6| \le 0.1$.
Jun
18
awarded  Generalist
Jun
18
answered How can I use a precise definition to find values of delta that correspond with given epsilon values
Jun
18
comment Numerically finding eigenvalues of a Volterra operator of first kind
I should amend: Potentially unstable
Jun
18
comment Numerically finding eigenvalues of a Volterra operator of first kind
You could try discretizing with respect to a basis for which each integral can be computed exactly. You should also check if the operator is normal; if not then the eigenproblem is numerically unstable.
Jun
18
comment Numerically finding eigenvalues of a Volterra operator of first kind
To be more explicit: There will be a band of 1s, but it should lie above the diagonal, not on it.
Jun
18
comment Numerically finding eigenvalues of a Volterra operator of first kind
If you are using a cutoff value, then you cannot choose discretization points near that cutoff value, because then the approximation will not be good. So your matrix should not be triangular in the traditional sense.
Jun
17
comment Numerically finding eigenvalues of a Volterra operator of first kind
What quadrature rule are you using?
Jun
12
revised How can I solve what kind of function this is?
correction
Jun
12
comment How can I solve what kind of function this is?
You're right, I was implicitly assuming here that $f \in L^{\infty}$.
Jun
12
answered How can I solve what kind of function this is?