Algebra Etc.

Tweets about algebra, number theory, and miscellaneous math by @JohnDCook.

[Algebra Etc. @AlgebraFact]

It is unknown whether the number of Mersenne primes is finite.

[Algebra Etc. @AlgebraFact]

Kan's paper introducing adjoint functors https://t.co/iKdIpW90s8 [pdf]

[Algebra Etc. @AlgebraFact]

Five points determine a conic section https://t.co/c4GFZL0Ppf

[Algebra Etc. @AlgebraFact]

The popular Mersenne Twister random number generator is so named because its period is a Mersenne prime.

[Algebra Etc. @AlgebraFact]

New post: The number of points on an elliptic curve

https://t.co/j1cvjrvXID

[Algebra Etc. @AlgebraFact]

A matrix Q is orthogonal iff it has orthonormal columns (or rows).

[Algebra Etc. @AlgebraFact]

The NIST elliptic curves have been in the news twice lately.

https://t.co/1b2RxB6xo5

[Algebra Etc. @AlgebraFact]

For n >= 5, the alternating group A_n is simple.

[Algebra Etc. @AlgebraFact]

Greco-Latin squares and magic squares https://t.co/o4riY5Y22N

[Algebra Etc. @AlgebraFact]

Volume to Area ratio for Regular Solids

https://t.co/Vb3576fghT

[Algebra Etc. @AlgebraFact]

If matrices A and B commute, then exp(A + B) = exp(A) exp(B).

[Algebra Etc. @AlgebraFact]

How NASA used Hadamard matrices to transmit photos from Mars

https://t.co/hyk8b5jGGa

[Algebra Etc. @AlgebraFact]

An n x n matrix A is non-singular iff the system Ax = b is consistent for all b.

[Algebra Etc. @AlgebraFact]

A subgroup N of G is normal if g^{-1}Ng = N for all g in G.

[Algebra Etc. @AlgebraFact]

New post: Refactoring Factorials

https://t.co/85oOckeOEw

[Algebra Etc. @AlgebraFact]

An n × n real matrix B has a real logarithm if and only if B is nonsingular and for each negative eigenvalue λ and each positive integer k the number of k × k Jordan λ-blocks occurring in the Jordan form of B is even.

[Algebra Etc. @AlgebraFact]

Every positive integer can be written as a sum of distinct Fibonacci numbers.

[Algebra Etc. @AlgebraFact]

Geometric equations written as determinants with a column of 1s https://t.co/bjoQe9NRGS

[Algebra Etc. @AlgebraFact]

If 2^p - 1 is prime, 2^{p-1}(2^p - 1) is an even perfect number. Euclid, Prob IX.36.

[Algebra Etc. @AlgebraFact]

An n x n matrix A is non-singular iff dim(range(A)) = n.