- vectors are writen in column format usually.
- A vector space
is obtained by equipping vectors with the operations of + and
by scalar.
- A nonempty subset
of a vector space
, x, y
.
- span(S) is the set of all possible linear combinations of the vectors in S = {
} forms a subspace.
- Linearly independent if no vectors in the collection can be expressed as a linear combination of the others.
- A basis of
is a set of
of vectors of minimal cadinality, such that
. The cardinality of a basis is called the dimension of
where
is a given point and
- A line is a one-dimensional affine set. The line through
along direction
is the set
, where in this case span(u) = {
}.
直线长度
- p = 2 is the standard Euclidean length
- p = 1 is the sum-of-absolute-values length
- p =
defines the
is the cardinality of a vector x.
(pseudo) norm.
