Examples
- When children find the answers to sums such as 4+3 or 4−2 by counting right or left on a number line, they are treating the number line as a one-dimensional affine space.
- Any coset of a subspace of a vector space is an affine space over that subspace.
- If is a matrix and lies in its column space, the set of solutions of the equation is an affine space over the subspace of solutions of .
- The solutions of an inhomogeneous linear differential equation form an affine space over the solutions of the corresponding homogeneous linear equation.
- Generalizing all of the above, if is a linear mapping and y lies in its image, the set of solutions to the equation is a coset of the kernel of, and is therefore an affine space over .
Read more about this topic: Affine Space
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)