Hi,

What I wrote is not wrong but I have been a little sloppy with the notation. I said ‘do linear transformations independently in the domain and range’ which implies that I am using two different bases. However I did not choose different notations for them. It would have been more precise (and less confusing?) if I had put primes on the basis vectors with indices 2 to n.

]]>Just one more technical remark: in general, I guess, the range and the nullspace of N are not complimentary (this is true however if N^2 = N, i.e. N is a kind of projections). That would mean that if e_1 spans the nullspace, that wouldn’t automatically imply that e_2, …, e_n span the whole range. But I guess you’re interested just in e_1 anyway. Please correct me if I’m wrong.

Yours.

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