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Vector

## Overview#

Vector is for most programming purposes a an array.

### Programing Languages #

Programing Languages often treat Vectors and Arrays as different Objects

We all need a little context:

• Physicists think of Vectors as arrows in space with a length and a direction.
• Computer scientists think of Vectors as ordered lists of numbers.
• mathematicians seeks to generalize both these views saying that a Vector can be anything where there's a sensible notion of adding two Vectors and multiplying a Vector by a number operations. Details of this view are rather abstract.

Vector is a arrow inside a x - y plane or an x-y axis rooted at their intersection.

Vector is a pair of numbers that basically gives instructions for how to get from the tail of that Vector at the origin to its tip the first number tells you how far to walk along the:

• x axis - Where positive numbers indicating rightward motion negative numbers indicating leftward motion.
• y-axis - The second number tells you how far to walk parallel to the y-axis. Where after that positive numbers indicating upward motion and negative numbers indicating downward motion.

### Euclidean Vector#

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric[1] or spatial vector,[2] or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B,[3] and denoted by {\displaystyle {\overrightarrow {AB}.} {\overrightarrow {AB}.

### Vector Space#

Vector may refer to a is a collection of objects called Vectors, which may be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also Vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of Vector addition and scalar multiplication must satisfy certain requirements, called axioms.

### Matrix#

is a set of Vectors