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Math Help - Question about the meaning of the words "Identity" and using them with Matricies

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    Question about the meaning of the words "Identity" and using them with Matricies

    What is an identity exactly? I hear the phrase “Additive Identity” which is something you add to a number that does not change its value. However, if I have 1 + 0 = 1, I assume 0 is the “Additive Identity” and the “Identity” is 1 correct?

    Also, I see a reference to the “Identity Matrix” but it seems like this is really the “Multiplicative Identity matrix” correct? Since there is also an Additive Identity Matrix (all zeroes). Does this make sense? And in this case, wouldn’t the “Identity” just be the Matrix itself?

    I am just trying to clarify the usage of the terms.
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    You must let go of this "add to a number". Do your best to think a bit more abstractly.

    Something + (Additive Identity) = Something -- The "Something" is mapped to itself - however addition is defined.

    The argument for multiplication is very similar.
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    Quote Originally Posted by Slappydappy View Post
    What is an identity exactly? I hear the phrase “Additive Identity” which is something you add to a number that does not change its value. However, if I have 1 + 0 = 1, I assume 0 is the “Additive Identity” and the “Identity” is 1 correct?
    No, not correct. a+ 0= a for a any number. That is why, for ordinary arithmetic, 0 is the "additive identity"- there is no name for the "a" since it could be any number. 1 happens to be the "multiplicative identity" for ordinary arithmetic but that is not because of "1+ 0= 1", it is because 1(a)= a for a any number.

    Also, I see a reference to the “Identity Matrix” but it seems like this is really the “Multiplicative Identity matrix” correct? Since there is also an Additive Identity Matrix (all zeroes). Does this make sense? And in this case, wouldn’t the “Identity” just be the Matrix itself?
    "The matrix itself"? What matrix are you talking about? Yes, what is normally called the "identity matrix" is the multiplicative identity for matrices. I suspect that is because multiplication of matrices is normally more important than addition in applications.

    I am just trying to clarify the usage of the terms.
    I am not sure I am understanding you. You seem to have the idea that isn "a+ O= a", O is the "additive identity" and a is the "identity" or that in "a(I)= a", I is the multiplicative identity and a is the "identity". That is incorrect. In the first O is the additive indentity and in the second I is the multiplicative identity but "a" does not have any special name because it could be anything. We just sometimes use the term "identity" withput the "multiplicative" or "additive" when (we hope) it is clear which we mean.
    Last edited by HallsofIvy; March 1st 2011 at 03:11 AM.
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