Definition: A scalar-formally is a mathematical concept in functional analysis, particularly with regard to vector spaces and their inner product. It refers to a linear map that satisfies certain properties that allow it to be represented as a sum of a scalar multiple of one element of the space and another, which makes it easier to work with and understand. In essence, a scalar-formally maps each element in a vector space into an element of the same space while preserving all its structure. This property is crucial for many applications
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