Michael Joyce

New Orleans, LA

math.tulane.edu/~mjoyce3

Age: 36

I am interested in algebraic combinatorics, especially in the combinatorics of orbits of a Borel subgroup on spherical varieties.
Jan
23
comment Combinatorics using a geometric diagram
I assume that in each step you have to move a given row to the row below it? There are multiple ways to interpret what a path is, as written.
Jan
23
comment Proving that $(u+v)×w=u×w+v×w$
If you don't know the number of dimensions, how do you expect us to know the number of dimensions? This sounds like a question of clarification that you should ask your instructor. (That said, the cross product is normally only defined for vectors in $\mathbb{R}^3$, so that's probably a pretty safe assumption. If you don't know the definition of cross product in $\mathbb{R}^3$, you'll surely need to look it up to construct a proof.)
Jan
22
comment Proving that $(u+v)×w=u×w+v×w$
How about writing out the components of the vectors $\vec{u}, \vec{v}, \vec{w}$ and computing each side?
Jan
21
answered Why does eliminating from linear equations work but adding them does not?
Jan
16
revised How to find critical points of the following polynomial?
fixed numerous grammatical and spelling errors
Jan
14
revised Is there a standard name for this poset
added 49 characters in body
Jan
14
comment Is there a standard name for this poset
I guess I abuse language and would call this the Bruhat order. Or I might call it the $Gr(k,n)$-Bruhat order. I think this is what most of the Schubert calculus world would do, but there may be a different name in other contexts.
Jan
14
answered Is there a standard name for this poset
Dec
26
comment Confusion regarding derivation of triangle inequality from Schwarz' inequality
Glad you got it sorted out! Cheers.
Dec
26
answered Confusion regarding derivation of triangle inequality from Schwarz' inequality
Dec
26
revised Confusion regarding derivation of triangle inequality from Schwarz' inequality
fixed formatting
Dec
19
awarded Constituent
Dec
10
awarded Excavator
Dec
8
awarded Caucus
Dec
5
comment Mrs Reed safe combination
Answer: 1. Mrs. Reed texts Mr. Reed, who remembers the combination. A malicious attacker would only need to try 84 combinations to open her safe with that information.
Nov
25
answered Choosing schedule for courses
Nov
24
comment If $T(v)=0$ for all $v \in V$, then $T=0$.
Let $v_1, v_2, \dots, v_n$ be any basis of $V$. Then the $j$-th column of the matrix representing T in this basis contains the coefficients of the expression of $T(v_j)$ in this basis. But $T(v_j) = 0 = 0 v_1 + 0 v_2 + \cdots + 0 v_n$, so that means the $j$-th column of the matrix is all zeroes. Since that is true for all $j$, the entire matrix consists of zeroes. Thus $T$ is represented in any basis by the zero matrix.
Nov
24
comment If $T(v)=0$ for all $v \in V$, then $T=0$.
Are you asking if $T(v) = 0$ for all $v \in V$, then the matrix representing $T$ in any basis is the zero matrix? That would, at least, be less tautological than the question you are asking.
Nov
21
comment How should I teach linear algebra and vector geometry together at high school?
What is the length of time you have to cover this material? If you are going to teach matrices, I'd spend a lot of time on the different ways to interpret matrix multiplication. Most students only learn that each entry is a dot product of a row and a column (worse, they often are only aware of the equivalent formula and have no understanding of where it comes from). Knowing that $A\vec{x}$ is both a linear combination of the columns of $A$ and the vector whose components are the dot products of rows of $A$ and $\vec{x}$ is really crucial to understanding everything else in linear algebra.
Nov
21
revised Null Space of Transformation
added 56 characters in body
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