20,809 reputation
11341
bio website drexel.edu/math/contact/ta-ra/…
location United States
age 24
visits member for 1 year, 1 month
seen 3 hours ago

I am pursuing a PhD in mathematics at Drexel university in Philadelphia, PA. I started my Teaching assistantship in fall 2013. As of now, I am not sure where my interests lie, though I am leaning towards something along the lines of matrix analysis.

I'm here because I enjoy being a part of the MSE community, and because whether you're asking or answering, you can never get enough practice with math problems.

Some answers I had fun putting together:

Some of my favorite questions/answers:

Useful links:


7h
comment Question about proving a real number
Note that the partial sums are a monotonically increasing sequence
19h
comment Trace of symmetric positive semidefinite matrix when diagonalized (as a bilinear form) in a non-orthogonal basis
@AlgebraicPavel whoops thanks
19h
comment Trace of symmetric positive semidefinite matrix when diagonalized (as a bilinear form) in a non-orthogonal basis
@user126154 I'm aware, and it's a strange thing to write, so I'm attempting to verify that this is what he meant.
19h
comment Trace of symmetric positive semidefinite matrix when diagonalized (as a bilinear form) in a non-orthogonal basis
@user161825 yes it is, $tr(U^{-1}SU) = tr(S)$.
19h
comment Trace of symmetric positive semidefinite matrix when diagonalized (as a bilinear form) in a non-orthogonal basis
Wait a second, so if $V$ is not orthogonal, do you mean $V^T S V$ is diagonal, or $V^{-1}SV$ is diagonal?
1d
answered Nullity of a matrix
1d
answered prove the following $(A^t)^{-1}=(A^{-1})^t$
1d
comment Prove that there is a basis of a lattice $\Lambda$ s.t. a reflection is of a certain form
@stebu92 I'm not actually sure what it means for a set to be a basis of $\Lambda$ as opposed to one of the general space, so if you could clarify this in either a comment or the question, it would help.
1d
comment Prove that there is a basis of a lattice $\Lambda$ s.t. a reflection is of a certain form
@stebu92 why would a basis of $\Bbb R^2$ not be a basis of $\Lambda$?
1d
answered Prove that there is a basis of a lattice $\Lambda$ s.t. a reflection is of a certain form
1d
answered Question about proving symmetric matrices are diagonalizable
1d
revised Question about proving symmetric matrices are diagonalizable
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1d
comment $\ker(A)=\text{Im}(A^*)^\perp$
Why are you having trouble applying what you've done? A matrix $A$ is a linear operator from $\Bbb C^n$ to $\Bbb C^n$, and $\Bbb C^n$ under the usual inner product is certainly a Hermitian space.
1d
comment Number of open sets in a metric space
@Anupam that's not what I had in mind, but it certainly works! At any rate, you have your answer then. $36$ is not a power of $2$, so no.
1d
answered Number of open sets in a metric space
1d
revised For What Values Of $x$ Is $f$ Continuous
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1d
revised Whether $\sum_{i=1}^k\frac{\prod_{j\neq i}(\alpha_j-\beta)}{\prod_{j\neq i}(\alpha_j-\alpha_i)}=1$ is true
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2d
comment Rank Nullity Theorem application
@Soaps the example shows it's not closed under addition
2d
answered Rank Nullity Theorem application
2d
answered having trouble with a characteristic polynomial and minimal polynomial question