Field
The next simplest example is the field F itself. Vector addition is just field addition and scalar multiplication is just field multiplication. Any non-zero element of F serves as a basis so F is a 1-dimensional vector space over itself.
The field is a rather special vector space; in fact it is the simplest example of a commutative algebra over F. Also, F has just two subspaces: {0} and F itself.
Read more about this topic: Examples Of Vector Spaces
Famous quotes containing the word field:
“Mine was, as it were, the connecting link between wild and cultivated fields; as some states are civilized, and others half-civilized, and others savage or barbarous, so my field was, though not in a bad sense, a half-cultivated field. They were beans cheerfully returning to their wild and primitive state that I cultivated, and my hoe played the Ranz des Vaches for them.”
—Henry David Thoreau (1817–1862)
“When it had long since outgrown his purely medical implications and become a world movement which penetrated into every field of science and every domain of the intellect: literature, the history of art, religion and prehistory; mythology, folklore, pedagogy, and what not.”
—Thomas Mann (1875–1955)
“I would say that deconstruction is affirmation rather than questioning, in a sense which is not positive: I would distinguish between the positive, or positions, and affirmations. I think that deconstruction is affirmative rather than questioning: this affirmation goes through some radical questioning, but it is not questioning in the field of analysis.”
—Jacques Derrida (b. 1930)