Vector Space
The set of all column n-vectors
The vector
Property:
The vector
It is a vector having the same magnitude as
Property: for any vector
Let V be a set on which the operations of addition and scalar multiplication are defined.[3]
The set V together with the operations of addition and scalar multiplication is said to form a vector space if the following axioms are satisfied:
Vectors in this case are continuous real-valued functions.
A polynomial of degree k (k≥0) is a function of the form
Let V be a vector space (for example,
To show that a subset S of a vector space forms a subspace, we must show that
If
Nonzero vectors
Let
Let
If V is a vector space with dim V = n > 0, then
If V is a vector space with dim V = n > 0, then
Given vector
Given vector
Changing coordinate vectors from one basis {
For an m×n matrix A, the rows are n-vectors from
Let
Let