Michael Joyce

New Orleans, LA

math.tulane.edu/~mjoyce3

Age: 37

I am interested in algebraic combinatorics, especially in the combinatorics of orbits of a Borel subgroup on spherical varieties.
2d
comment Isomorphism matrix problem
@Kior: Your reasoning for (A) is sound: since $T$ is not bijective, it cannot be an isomorphism. For (B), you cannot argue based on thinking that something is or is not right. You need to check each part of the definition of an isomorphism. Is $T$ a linear transformation? Is $T$ bijective? Similarly, for (C) and (D), you must verify the conditions. You should not consider any answer you come up with to be "right" unless you have a well-reasoned argument in support of your conclusion.
2d
comment Isomorphism matrix problem
@MarcvanLeeuwen: Actually the map in (C) is not linear.
2d
comment Algebraic confusion
The simplification is obtained by finding a common denominator for the expression inside brackets.
Feb
9
comment F is a vector space and U, V, and W are subspaces of F. Prove that $U\bigcup V\bigcup W$ is a subspace of F if and only if $U,V\subset W $.
False: $U = V = F$, $W = \{0\}$.
Feb
8
comment showing projection is a linear operator
I think you mean that $\alpha y_1 + \beta y_2 \in Y$. Can you show that $\alpha z_1 + \beta z_2 \in Y^{\perp}$?
Feb
8
answered Complex Analysis Lectures
Feb
7
comment Prove that elementary matrices perform row operations
Proof of what?
Feb
5
awarded Strunk & White
Feb
5
awarded Custodian
Feb
5
reviewed Edit and Reopen What is the length of the 4th side?
Feb
5
revised What is the length of the 4th side?
deleted 1 character in body
Feb
5
reviewed Close If $X$, $Y$ are random variables such that $E(X\mid Y=y)$ is constant for all $y$, then show that $E(XY)=E(X)E(Y)$ [i.e.,$\text{Cov}(X,Y)=0$]
Feb
5
reviewed Leave Open which of the following functions are differentiable at x=0
Feb
5
reviewed Close Symmetric $3 \times 3$ Matrix
Feb
5
revised adding rows together linear algebra
added 12 characters in body
Feb
4
awarded Nice Question
Feb
4
awarded Scholar
Feb
4
comment What's the most effective way to introduce/motivate the anti-derivative of $\sec x$?
Thanks! Both of your suggestions are good ones, but I've accepted this one as it is a bit more concrete in answering my question.
Feb
4
accepted What's the most effective way to introduce/motivate the anti-derivative of $\sec x$?
Feb
3
comment Student converted $\sqrt{x^2}$ and ended up with just $x$ instead of $|x|$
@DanielR.Collins: Good point!
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