Determine the dimension of ker(T)?
2015-03-13 4:40 am
For a positive integer n>1, let T:M_(nn) ->R be the linear transformation defined by T(A) = tr (A), where A is an nxn matrix with real entries. Determine the dimension of ker(T)
回答 (1)
2015-03-13 5:30 am
✔ 最佳答案
Clearly the image of T is all of R, so its rank is 1. By rank-nullity, the nullity, i.e. the dimension of the kernel, is the dimension of the domain minus the rank, namely n^2 - 1.
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