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Math Help - What is the dimension of M(2x2) over K? Find basis? (linear algebra)

  1. #1
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    What is the dimension of M(2x2) over K? Find basis? (linear algebra)

    M(2x2)(R) is a vector space of K.
    M =
    (a......b)
    (-b.....a)
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  2. #2
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    Tejas
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    Re: What is the dimension of M(2x2) over K? Find basis? (linear algebra)

    one way of thinking of a basis is it tells us: "how many pieces of information we need to specify". how many numbers (scalars) do you have to know to completely determine the matrix:

    \begin{bmatrix}a&b\\-b&a \end{bmatrix}?

    can you write the matrix as:

    a*something + b*(another something)?

    what might the "somethings" be?
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