Let me start by defining the Identity Matrix In.
Definition 1: In: Identity Matrix for n x n matrix
The Identity Matrix for n is an n x n matrix consists of values [ai,j] where i = the row and j = column where:
i = j → ai,j = 1
i ≠ j → ai,j=0
Here are a few examples:
If An,n is an n x n matrix, we have:
Property 1: An,nIn = An,n
Proof:
(1) Let:
(2) Then, An,nIn =
QED
Property 2: InAn,n = An,n
Proof:
(1) Let:
(2) Then, InAn,n =
QED
If An,m is an n x m matrix, we have:
Property 3: An,mIm=An,m
(1) Let:
(2) Then, An,mIm =
QED
References
- "Identity Matrix", Wikipedia.org
5 comments :
I just found this post using google and I just wanted to thank you for it. Your blog is awesome and I hope you continue to do this (you straightfowardly explained something in my math homework that I just could not understand, even with the help of my math buddies). Thanks again, hope you continue to do this.
Thanks very much for the feedback. I am very glad that my blog helped. :-)
Cheers,
-Larry
your blog rocks thanks, you da man
this is fantastic
helps me with proofs alot!
I am a PhD econ student who has returned to school after many years of working. This is a lifesaver for picking up the details that many advanced proofs skip. Thanks a million!!!
Post a Comment