How do I show that column equivalence on the set of all $m\times n$ matrices is an equivalence relation?
I know that to show it is an equivalence relation, I need to show that column equivalence is transitive, symmetric, and reflexive.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this communityHow do I show that column equivalence on the set of all $m\times n$ matrices is an equivalence relation?
I know that to show it is an equivalence relation, I need to show that column equivalence is transitive, symmetric, and reflexive.
Hint: the expression "column equivalence" does most of your work for you.
I know that to show it is an equivalence relation, I need to show that column equivalence is transitive, symmetric, and reflexive.
Just do exactly that: show that your column equivalence is transitive, symmetric, and reflexive on the set of all $m\times n$ matrices. To do this:
Review your notes and/or text as reference, and answer:
If you can answer "yes" to each of the above, then we've established that column equivalence on $m\times n$ matrices is an equivalence relation.
Unpacking the definitions of the properties of an equivalence relation is key here, along with the fact that the relation in question is defined as "column equivalence".