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Martin Sleziak
Martin Sleziak
1:46 PM
new-tag A new tag verbal-subgroups was created by Yanior Weg. There is also a pending suggested edit for the tag-excerpt.
1
Q: Is it true, that for any two non-isomorphic finite groups $G$ and $H$ there exists such a group word $w$, that $|V_w(G)| \neq |V_w(H)|$?

Yanior WegIs it true, that for any two non-isomorphic finite groups $G$ and $H$ there exists such a group word $w$, that $|V_w(G)| \neq |V_w(H)|$? Here $V_w(G)$ stands for the verbal subgroup of $H$, generated by the group word $w$. Initially, the question I wanted to ask was: β€œIs it true, that for any tw...

abstract-algebra group-theory finite-groups group-varieties verbal-subgroups
 
 
4 hours later…
Martin Sleziak
Martin Sleziak
6:00 PM
new-tag A new-tag column-stochastic-matrix was created by Markov (formerly Wow). I'd guess that this is covered by the already existing stochastic-matrices tag.
0
Q: Does always a $B$ with orthonormal rows/column be found so that $BP=0$?

MarkovI am given, $P_{n\times n}$ column stochastic, I need to see whether a matrix of suitable order $B$ with an orthonormal column or rows can be constructed so that $BP=0$? I started trialing like this: $\begin{bmatrix}b_{11}&b_{12}\\ b_{21}&b_{22}\end{bmatrix} \begin{bmatrix}p_{11}&p_{12}\\ p_{21}&...

linear-algebra orthonormal column-stochastic-matrix
Stochastic matrix
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix.The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics.There are sever...
Doubly stochastic matrix
In mathematics, especially in probability and combinatorics, a doubly stochastic matrix (also called bistochastic), is a square matrix A = ( a i j ) {\displaystyle A=(a_{ij})} of nonnegative real numbers, each of whose rows and columns sums to 1, i.e., βˆ‘ i a i j = βˆ‘ ...
@MartinSleziak The suggested edit was approved, so now there is a tag-excerpt for verbal-subgroups.
 

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