Definition
The dot product is often defined in one of two ways: algebraically or geometrically. Equivalence of these definitions is proven later.
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“One definition of man is an intelligence served by organs.”
—Ralph Waldo Emerson (18031882)
“Im beginning to think that the proper definition of Man is an animal that writes letters.”
—Lewis Carroll [Charles Lutwidge Dodgson] (18321898)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (17721834)