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Thread: [RESOLVED] What is the true nature of a one-by-one matrix?

  1. #1

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    Resolved [RESOLVED] What is the true nature of a one-by-one matrix?

    Hello everyone.

    We all know that a matrix can have m rows and n columns.
    However, in the very special case of m = n = 1 we have a one-by-one matrix.

    Question is, what is the true nature of a one-by-one matrix?
    Is it conceptually the same thing as the number in it?
    Or is it a different creature?

    For example can I write:
    [5] = 5
    [k + r] = k + r
    If I were to draw an analogy, for example with sets, a set containing only one element is not the same thing as that element alone.
    But, it looks like with matrices, the one-by-one matrix is the same as the element inside it.
    Is this true?
    If yes, why so different from sets?
    If no, why?

    I would appreciate it if anybody could shed some light on this issue.
    Thanks.

  2. #2
    Fanatic Member Delaney's Avatar
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    Re: What is the true nature of a one-by-one matrix?

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  3. #3

    Re: What is the true nature of a one-by-one matrix?

    So, here's the deal with a one-by-one matrix, or as some people call it, a scalar. It's basically just a fancy way of saying that the matrix has only one number in it.
    When you see something like [5] = 5 or [k + r] = k + r, it means you're treating that one-by-one matrix as if it's just a regular number. And you know what? That's totally cool because that one entry in the matrix represents the whole thing. So, in this case, the one-by-one matrix is basically the same as the scalar value.
    Now, the reason we make this distinction between sets and matrices has to do with their different mathematical structures. Sets and matrices have different purposes and different things you can do with them. Matrices are all about linear transformations and solving systems of equations, while sets are more about grouping objects together.

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    Re: What is the true nature of a one-by-one matrix?

    Thanks for the help.
    Ilia

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