Vector
Dependencies:
- Ring optional
A vector $v$ is a sequence of numbers. The $i^{\textrm{th}}$ element in the sequence is denoted by $v_i$. The number of elements in the vector is called the length or size of the vector.
The elements of a vector are generally real numbers. Such vectors are called real-valued vectors. However, there can be vectors of other types, like vectors of integers, vectors of complex numbers and vectors of rings or fields. (Ring and field are concepts from abstract algebra.)
The set of all vectors of length $n$ whose elements are from the set $S$ is denoted by $S^n$. Consequently, the set of vectors of real numbers of length $n$ is denoted by $\mathbb{R}^n$.
The sum of two vectors is defined as their element-wise sum: \[ (u + v)_i = u_i + v_i \]
Scalar multiplication is defined as follows: \[ (cv)_i = cv_i \]
Dependency for:
Info:
- Depth: 2
- Number of transitive dependencies: 2