qudt:Vector

A Vector is an array data type that can have a dimensionality of one, or more elements. Vectors can represent physical quantities, such as velocity, force, displacement; mathematical objects such as points or directions in space; and abstract representations for things such as colors, features, or embeddings in computational contexts.

As a one-dimensional mathematical object it can represent a quantity with both magnitude and direction in space. One-dimensional vectors can be thought of as a special case of a 1D array. For example a 3D vector can be expressed as a list of coordinates: [x,y,z].

A vector in n-dimensional space can represent a point, a direction, or a linear combination of basis vectors.

Vectors can represent quantifiable values. For example a car moving at 60 m/hr to the north, assuming north is along the y-axis, can be represented in 2D as:

[0, 60]

In machine learning a Feature Vector can be expressed for a dataset entry as:

[5.1, 3.5, 1.4, 0.2]

In AI for text processing a Word Embedding Vector is expressed as a N-dimensional space, where N can be a large number.