Let T be a linear operator on a Hilbert space. Then is called an Eigen
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De nition 21Let T be a linear operator on a Hilbert space Then Essay
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values of T if there exist a non zero vector v .
Let T be a linear operator on a Hilbert space. Then the non zero vector
v 2 H is said to be an Eigen vector of T if there exists a scalar such that
vT = v .
Let be an eigen value of T and let M be the set of all eigen vectors of T
corrseponding to the eigen value together with the zero vector.
Then M is called
the Eigen Space of T corresponding to .
It is denoted by M = f v : (T- I ) v =0g
If T is normal,then v is an eigen vector of T with eigen value if and only
if v is an eigen vector of T with eigen value .