Let T be a linear operator on the the finite dimensional space V, and let R be the range of T.(adsbygoogle = window.adsbygoogle || []).push({});

(a) Prove that R has a complementary T-invariant subspace iff R is independent of the null space N of T.

(b) If R and N are independent, prove that, N is the unique T-invariant subspace complementary to R.

I supposed R has a complementary T - invariant subspace, say, W. Then , R should be T- admissible. I assumed to the contrary, that R intersection T is not equal to {0}. I took a point in the intersection but could not proceed further. Please suggest.

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# Cyclic decompostions

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