Can't you use algebra to solve for all possible values of T?broncos#1 said:I am trying to to find examples where <T(v),v>=0 where the operator is not 0
A positive non-self adjoint operator is a mathematical object that represents a linear transformation between two vector spaces, where the operator is not equal to its adjoint. Additionally, the operator is positive, which means that it maps positive vectors to positive vectors.
A positive non-self adjoint operator differs from a positive self-adjoint operator in that it does not possess the symmetry property of being equal to its adjoint. This means that the operator maps vectors to a different space than its adjoint does, and it may also have complex eigenvalues.
Positive non-self adjoint operators have many applications in mathematics, physics, and engineering. They are used to model phenomena such as heat flow, fluid dynamics, and quantum mechanics. They are also used in numerical analysis to solve differential equations and in optimization problems.
Positive non-self adjoint operators are a special case of Hermitian operators, which are self-adjoint and have real eigenvalues. However, positive non-self adjoint operators may have complex eigenvalues and are not equal to their adjoints. Hermitian operators also have additional properties, such as orthogonality of eigenvectors.
No, positive non-self adjoint operators are defined as operators that map positive vectors to positive vectors. This means that they can only have positive or zero eigenvalues. If a positive non-self adjoint operator has a negative eigenvalue, it would violate this definition and would instead be classified as a negative operator.