What is the defect of a linear transformation

[gruba]

Homework Statement

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?

 

[S.G. Janssens]

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.