Is Adjoint Operator Linear?
[Edit] Existence of the Adjoint When T Is a Bounded Operator (Hence D(T) = H) Then It Can Be Shown, Again Using the Riesz Representation Theorem, That T∗ Is...
How do you know if an operator is linear?
- f(x+y)=f(x)+f(y) for all x and y;
- f(cx)=cf(x) for all x and all constants c.
How do you find the adjoint of a linear operator?
We have that 〈x,T(y)〉 = 〈T(y),x〉 = 〈y,T∗(x)〉 = 〈T∗(x),y〉. Let A = (aij ) be an m × n matrix with complex entries. The adjoint matrix of A is the n × m matrix A∗ = (bij ) such that bij = aji . That is, A∗ = At.
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