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:
“the whole field is a
white desire, empty, a single stem;
a cluster, flower by flower,
a pious wish to whiteness gone over—
or nothing.”
—William Carlos Williams (1883–1963)
“When white men were willing to put their own offspring in the kitchen and corn field and allowed them to be sold into bondage as slaves and degraded them as another man’s slave, the retribution of wrath was hanging over this country and the South paid penance in four years of bloody war.”
—Rebecca Latimer Felton (1835–1930)
“... there are no chains so galling as the chains of ignorance—no fetters so binding as those that bind the soul, and exclude it from the vast field of useful and scientific knowledge. O, had I received the advantages of early education, my ideas would, ere now, have expanded far and wide; but, alas! I possess nothing but moral capability—no teachings but the teachings of the Holy Spirit.”
—Maria Stewart (1803–1879)