- #1
Saladsamurai
- 3,020
- 7
Homework Statement
If a diagonal matrix is a square nxn matrix whose only nonzero entries occur in positions [itex]a_{ii},\ i=1,2,...,n[/itex] prove that the product of two nxn diagonal matrices, D1 and D2, is diagonal AND that D1 and D2 commute.
(HINT: Use D1=[[itex]d_{ij}[/itex]] and D2=[[itex]d'_{kl}[/itex]]
use the defintion of matrix multiplication to show that there is at most one non zero term in [tex]c_{il}=\sum_jd_{ij}d'_{jl}[/tex])
Homework Equations
Definition of matrix multiplication (This is where I have the most trouble)
For C=BA, [tex]c_{ik}=\sum_{k=1}^nb_{ik}a_{kj},\ i=1,...,m\ j=1,...,p[/tex]
So my biggest trouble stems from these really general definitions :yuck: I mean, I know they shouldn't be to difficult...I can multiply matrices with actual numbers in them, but this definition is giving me grief.
Can someone just kind of talk about this defintion with me for a minute? Then I can make a real attempt at a solution.
Thanks!