Let H be a Hilbert space and E c H be a subset of Н. (a) Show that E- is a closed linear subspace of H. (b) Show that (E-)- is the closed linear subspace of H spanned by E.

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A: False

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A: The answer is given below:

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A: our objective is to conclude.

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Q: Let H be a Hilbert space, then a closed linear subspace Mof H reduces an operator T if and only if M…

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A: We have to show that set of all skew symmetric matrix form subspace of Mnn

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Q: If T is a normal operator on a finite dimensional inner product space V and if W is a subspace of V…

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Q: 2. Provide an example of a subset U of V that is a subspace of V, as well as an example of subset W…

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Q: 2) Let H be a Hilbert space, express H as a direct sum of any two of its subspaces. Prove that the…

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Q: Please see image

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

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A:

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A: Given :Let p be the projection matrix corresponding to a subspace             S of RM

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A:

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Q: (b) Prove that if V is finite dimensional, then every subspace of V is also finite dimensional.…

A: (b)

Q: If X is an inner product space, and A is subspace of X then A = A+ True False

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A:

Q: If M is a closed subspace of a Hilbert space H then H %3DМӨМ'.Prove.

A: Complete inner product space is called Hilbert space

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Q: 12) Show that subset W of a vector space V is a subspace of V if and only if span(W) = W.

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Q: .

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Q: (a) A subspace Y of a Hilbert space H is closed if and only if Y = Y.

A: To Prove- A subspace Y of a Hilbert space H is closed if and only if Y⊥⊥ = Y.

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A: Here we get a counter example.

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A: V=M2X2R SPANNED BY A=1-5-42, B=11-15, C=2-4-57, D=1-7-51 Solution:- To find: A basis and the…

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Q: Let H be a Hilbert space, then a closed linear subspace Mof H reduces an operator T if and only if M…

A: