How this calculation works
Compute DA−AD when D is diagonal and determine whether the matrices commute.
THE FORMULA
[D,A]ᵢⱼ = (dᵢ−dⱼ)AᵢⱼA worked example
Diagonal values 2 and 5 multiply the upper entry 4 by −3, giving −12.
Good to know
The diagonal of this commutator is always zero.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Compute DA−AD when D is diagonal and determine whether the matrices commute.
The primary result is labeled “Upper commutator entry”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The diagonal of this commutator is always zero.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
Diagonal values 2 and 5 multiply the upper entry 4 by −3, giving −12.
Which rule does this calculator apply?
[D,A]ᵢⱼ = (dᵢ−dⱼ)Aᵢⱼ