Duplex Numbers

a ± b ± c

Calculator

add, extend or multiply duplex numbers and see the resulting distribution below

5
± 2 ± 1
1
=
Multiset / Bag
Underlying Set

Displayed in depth-first order (following minus before plus).

Statistical Properties

Consider the duplex number a ± b ± c

As such, any symmetrical distribution of numbers can be represented as the underlying set of a duplex number.

Eigenvalues

Duplex numbers can be used to find the eigenvalues for a 2x2 matrix. Consider the matrix: 

    | x  z |
    | v  y |
First, determine the two duplex numbers that represent the diagonals of the matrix, such that: 
    a±b = (x,y) and c±d = (v,z)

    a±b = (x+y)/2 ± |(x+y)/2-x|
    c±d = (v+z)/2 ± |(v+z)/2-v|
when b = d, the eigenvalues are: 
       a±c
when b ≠ d, the eigenvalues are: 
       a ± √(b² + c² - d²)