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.
6h
answered Choosing schedule for courses
1d
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.
1d
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
Nov
21
revised Null Space of Transformation
added 20 characters in body
Nov
21
answered Null Space of Transformation
Nov
17
comment Show that $x$, $y$, $z$ are integers when $3x$, $3x^2-6yz$, $x^3+2y^3+4z^3-6xyz$ are integers.
I think you intend to assume that $x, y, z \in \mathbb{Q}$?
Nov
14
revised $AB=BA$ with same eigenvector matrix
edited body
Nov
14
revised After removing any part the rest can be split evenly. Consequences?
edited tags
Nov
14
comment After removing any part the rest can be split evenly. Consequences?
Is it clear that the rank of $A$ over $\mathbb{Q}$ must be at least as great as its rank over $\mathbb{F}_2$?
Nov
13
comment What is the relationship between vector and its associated skew symmetric matrix?
Welcome! Hope you'll stick around and ask and answer many more questions in the future!
Nov
1
comment Let $A, B$ be $2\times 2$ matrices. Show that $AB = O$ but $BA \ne O$.
You need to edit your post to indicate what $A$ and $B$ are.
Oct
31
comment Math puzzle: 10 digit strings generations
Well if it is true that you can get the maximum number of strings possible for $(10,4)$, that property might hold for smaller pairs as well. Ideally, one might construct a proof of that property in the smaller cases that are easier to work with, and then find a way to generalize that proof to cover the case $(10,4)$.
Oct
31
comment Math puzzle: 10 digit strings generations
Have you studied the problem of $m$-digit strings without reusing any $n$-digit string for pairs $(m,n)$ smaller than $(10,4)$?
Oct
28
answered Why does this method of solution for this system of equations yield an incorrect answer?
Oct
28
answered determinants and invertible matrices
Oct
27
revised Limits-related question
edited tags
Oct
27
answered Getting the points at which the tangent plane is horizontal?
Oct
27
reviewed Approve suggested edit on Getting the points at which the tangent plane is horizontal?
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