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Math Help - Range of a Matrix (Applications)?

  1. #1
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    Question Range of a Matrix (Applications)?



    Hi

    What does the range of a Matrix indicate?
    Which are the applications in economy and operational research of the range of a matrix?

    Thanks
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by osodud View Post

    Hi

    What does the range of a Matrix indicate?
    Which are the applications in economy and operational research of the range of a matrix?

    Thanks
    The range of the matrix can be thought of as follows

    Each matrix A\in\text{Mat}_n\left(\mathbb{R}\right) is really a linear transformation A:\mathbb{R}^n\to\mathbb{R}^n. Then \text{ran }A=A\left(\mathbb{R}^n\right).

    I have no idea about the applications
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  3. #3
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    There are numerous applications, although I don't know enough about numerical economics to produce one in economics (I'm an Austrian economist myself, and their methodology is very different.)

    In operations research, though, one application of matrices is Markov chains. So, give one probabilistic state, the Markov transition matrix tells you what the new probabilities are after a state change. The range of the Markov matrix is equal to the set of possible states to which you can transition from an earlier state.
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