Real Line - As A Vector Space

As A Vector Space

The real line is a vector space over the field R of real numbers (that is, over itself) of dimension 1. It has a standard inner product, making it a Euclidean space. (The inner product is simply ordinary multiplication of real numbers.) The standard norm on R is simply the absolute value function.

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Famous quotes containing the word space:

    “The merit of those who fill a space in the world’s history, who are borne forward, as it were, by the weight of thousands whom they lead, shed a perfume less sweet than do the sacrifices of private virtue.”
    —Ralph Waldo Emerson (1803–1882)