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Can you rephrase the question? What is e ?

  1. Mar 31, 2005 #1
    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. jcsd
  3. Mar 31, 2005 #2


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    It is this symbol : [itex]\in[/itex]. [itex]A \in M_{n,n}[/itex] means that A is in the space of (n x n)-matrices. So, is the set [itex]S_B[/itex] of all (n x n)-matrices that commute with B a subspace of [itex]M_{n,n}[/itex]? 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 [itex]\in[/itex] 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.
  4. Mar 31, 2005 #3
    Yes. Read [itex] x \in y[/itex] as "[itex]x[/itex] is in [itex]y[/itex]" or "[itex]x[/itex] is an element of the set [itex]y[/itex]."

    Some other useful symbols are [itex]\exists[/itex] and [itex]\forall[/itex]. Read [itex]\exists[/itex] as "there exists", and [itex]\forall[/itex] as "for any," or "for all."

    These symbols are fairly ubiquitous in mathematics (as are many, many others).
    Last edited: Mar 31, 2005
  5. Mar 31, 2005 #4
    I'm retArdEd. Thanks!!! :rofl:
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