# Can you rephrase the question? What is e ?

1. Mar 31, 2005

### pattiecake

Can you rephrase the question? What is "e"?

Is {A e Mn,n | AB = BA for a fixed B e Mn,n a subspace of Mn,n? (where Mn,n is a matrix M, of dimension n by n)? Not having had a logic class, I have /no idea/ what this is asking...

I'm not even sure what the e is. Its a small capital e - looks like a greek letter. Equivalent to?

2. Mar 31, 2005

### AKG

It is this symbol : $\in$. $A \in M_{n,n}$ means that A is in the space of (n x n)-matrices. So, is the set $S_B$ of all (n x n)-matrices that commute with B a subspace of $M_{n,n}$? You should know of 3 things to test for to determine if it's a subspace (the subspace test) and using the basic axioms of matrix multiplication, you should be able to solve the problem. The symbol $\in$ is a set theoretic one that says that something is an element of a set. It's not really a logic symbol, it's one used in mathematics all the time. Seeing as how you're working with vector spaces, I'm surprised you've never seen it.

3. Mar 31, 2005

### Data

Yes. Read $x \in y$ as "$x$ is in $y$" or "$x$ is an element of the set $y$."

Some other useful symbols are $\exists$ and $\forall$. Read $\exists$ as "there exists", and $\forall$ as "for any," or "for all."

These symbols are fairly ubiquitous in mathematics (as are many, many others).

Last edited: Mar 31, 2005
4. Mar 31, 2005

### pattiecake

I'm retArdEd. Thanks!!! :rofl: