In mathematics, the

**Euclidean distance**or**Euclidean**metric is the "ordinary" straight-line**distance**between two points in**Euclidean**space. With this**distance**,**Euclidean**space becomes a metric space. The associated norm is called the**Euclidean**norm. Older literature refers to the metric as Pythagorean metric.In respect to this, what is the Euclidean norm of a matrix?

**Frobenius Norm**. The

**Frobenius norm**, sometimes also called the

**Euclidean norm**(a term unfortunately also used for the vector -

**norm**), is

**matrix norm**of an

**matrix**defined as the square root of the sum of the absolute squares of its elements, (Golub and van Loan 1996, p. 55).

Why do we use Euclidean distance?

The

**Euclidean Distance**tool is**used**frequently as a stand-alone tool for applications, such as finding the nearest hospital for an emergency helicopter flight. Alternatively, this tool can be**used**when creating a suitability map, when data representing the**distance**from a certain object is**needed**.What is the meaning of Euclidean space?

**Euclidean space**, In geometry, a two- or three-dimensional

**space**in which the axioms and postulates of

**Euclidean**geometry apply; also, a

**space**in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.