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Homework Help: What is the defect of a linear transformation

  1. Jan 21, 2016 #1
    1. The problem statement, all variables and given/known data
    Question: What is the defect of a linear transformation?
    2. The attempt at a solution
    A defective matrix (of a linear transformation) is a matrix that doesn't have a complete basis of eigenvectors.
    Does this mean that linearly dependent vectors of a matrix are called defects?
  2. jcsd
  3. Jan 21, 2016 #2


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    In general, the defect of a linear operator is the codimension of its range. For operators on finite dimensional spaces (represented by matrices), the rank theorem implies that the defect equals the nullity of the operator, where the latter is the dimension of the kernel.
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