Metric (mathematics)
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A metric is a function that give the distance, i.e. a real number, between any two elements of a space.
A metric may be induced from a norm as shown at: Section "Metric induced by a norm".
Because a norm can be induced by an inner product, and the inner product given by the matrix representation of a positive definite symmetric bilinear form, in simple cases metrics can also be represented by a matrix.