hardmath

Knoxville, TN

uclue.com

Age: 61

Enjoys programming in Prolog.

Richard O'Keefe: "Prolog is an efficient programming language because it is a very stupid theorem prover."

When I cross the street, I look both ways: up and dn.

5h
awarded Nice Question
6h
comment Is the Square Root of an Inverse Matrix Equal to the Inverse of the Square Root Matrix?
For real symmetric matrices $A$ you have articulated the necessary and sufficient condition: $A$ must be positive definite. For nonsymmetric matrices we can analyze the conditions in terms of the Jordan normal form and the spectrum (eigenvalues) of $A$. It's worth a new Question if you'd like to pursue that topic.
7h
comment Using Math.SE as a contest site
For comparison, Martin's link above to a previous Meta thread seems to correspond to this "contest" Question. The detailed rules set out there do not IMHO conflict with normal Community guidelines.
13h
comment Find the minimum, irreducible polynomial
So far, so good, but there is a factor $x+1$ to remove.
13h
comment Find the minimum, irreducible polynomial
Note that minimal polynomials over a field are necessarily irreducible.
15h
asked Using Math.SE as a contest site
16h
reviewed Approve suggested edit on Finding supremum in $S=\{q\in\Bbb Q:q<x\}$
16h
comment traffic flow: red/green light or stop and move?
... and the time to clear the intersection. It's a nice mathematical modelling problem, but more work is needed to identify and assign values to parameters to make it realistic. If the intention is to have the Readers perform the entire modelling exercise, it tends to make the problem less about the mathematics (queuing theory) and more about the Readers' imaginative faculties.
16h
comment Permutation Groups question in abstract algebra
Have you tried to apply the definition of a permutation? This is actually a rather nice result, useful in showing that every group can be embedded into a permutation group (and that every finite group can be embedded in a finite permutation group).
16h
comment Is there a surface S$\subset R^3$ whose Gaussian curvature is -1 at each point S?
I suspect any embedding of a pseudosphere/surface of constant negative curvature in $\mathbb{R}^3$ will have a singularity, as the tractricoid does (see illustration in article linked by Daniel above).
17h
awarded Sportsmanship
18h
reviewed Close Generator matrix of a Reed-Muller code
19h
revised Is the Square Root of an Inverse Matrix Equal to the Inverse of the Square Root Matrix?
punctuation fix
19h
revised Is the Square Root of an Inverse Matrix Equal to the Inverse of the Square Root Matrix?
fixed omissions
19h
answered Is the Square Root of an Inverse Matrix Equal to the Inverse of the Square Root Matrix?
20h
comment Is the Square Root of an Inverse Matrix Equal to the Inverse of the Square Root Matrix?
Note that in that article "positive definite" assumes (at least for real matrices) that the matrix is also symmetric. Thus a real symmetric positive definite matrix has a unique real symmetric positive definite matrix square root (which is the analog of taking the positive square root of a positive real number).
1d
comment Is the Square Root of an Inverse Matrix Equal to the Inverse of the Square Root Matrix?
There is a risk of misunderstanding in referring to "the" square root of a matrix, as matrix square roots are typically even less unique than square roots of scalars (where we have a choice of sign in picking a square root).
1d
comment Implicit function theoroem
I'm afraid your "statement" to be shown is unintelligible. In the case that a surface $F(x,y,z) = C$ can be "solved for any of the three variables (let's assume this to be in the neighborhood of some point $(x_0,y_0,z_0)$ on the surface), then any one of the three variables, say $x$, would have partial derivatives via Implicit Function Thm. with respect to the other two, say $y,z$. But in your notation it is unclear what "derivative" is meant.
1d
revised Row reduction and the characteristic polynomial of a matrix
edited tags
1d
revised Row reduction and the characteristic polynomial of a matrix
added example of row operations and computation of characteristic polynomial
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