equitable matrices of order 2


The most general 2×2 equitable matrix is of the form

M=(1λ1/λ1)

for some λ>0.

Let us consider the matrix

M=(m11m12m21m22).

A necessary and sufficient condition for M to be an equitable matrix is that m11,m12,m21,m22>0 and

m11=m11m11,
m11=m12m21,
m12=m11m12,
m12=m12m22,
m21=m21m11,
m21=m22m21,
m22=m21m12,
m22=m22m22.

It follows that m11=m22=1, and m12=1/m21.

Title equitable matrices of order 2
Canonical name EquitableMatricesOfOrder2
Date of creation 2013-03-22 14:58:30
Last modified on 2013-03-22 14:58:30
Owner matte (1858)
Last modified by matte (1858)
Numerical id 4
Author matte (1858)
Entry type Example
Classification msc 15-00