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Difference among types of bases.

  1. Dec 7, 2011 #1
    Hello everyone,

    I am currently learning about bases, and I am confused about different types of bases. I understand how to obtain a basis for the null space of A or a basis for the range of A. I recently ran into a problem that simply asked me to find a basis for A. What does this mean? Does it mean any basis (for N(A) or R(A))? OR is there such a thing as a separate basis for A not having to do with R(A) or N(A)?
  2. jcsd
  3. Dec 7, 2011 #2
    Maybe it wants you to visualize the set of matrices as a vector space?

    Consider for example the set of matrices of the form

    |a 0|
    |0 b|

    They are spanned by the two independent elements

    |1 0|
    |0 0|

    |0 0|
    |0 1|

    so this is a basis for the subspace of matrices given above. What is the exact form of A and of the question?
  4. Dec 7, 2011 #3
    If A is a matrix, the question is nonsense.

    If A is a vector space, then it makes sense.
  5. Dec 8, 2011 #4


    User Avatar
    Science Advisor

    my guess is what is meant is a basis for the column-space or row-space of A.
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