can eigen vector contain indefinite values
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An eigen value is basically a scalar which turns a vector operation into an algebraic one. For instance, when you have a differential equation in the form of an eigenvalue equation, it basically means that the rate of change of the function is directly related to the nature of the function itself. The eigenvalue provides the scale for the exact direct relation.
A vector has a unique eigen value with respect to a particular operator. In that sense, it can have infinite eigen values, each corresponding to a different operator.
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no it can not contain indefinite values
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