# VectorAround

VectorAround[{x1,x2,},{δ1,δ2,}]

represents a vector of uncorrelated approximate numbers or quantities with values xi and uncertainties δi.

VectorAround[{x1,x2,},{{Δ11,Δ12,},{Δ12,Δ22,},}]

represents a vector of approximate numbers or quantities with values xi and covariance matrix Δ.

VectorAround[{x1,x2},{{δ1,δ2},ρ}]

represents a pair of approximate numbers or quantities with uncertainties δ1, δ2 and correlation factor ρ.

VectorAround[{x1,x2,},{{δ1,δ2,},{{1,R12,},{R12,1,},}}]

represents a vector of approximate numbers or quantities with uncertainties δi and correlation matrix R.

# Details • VectorAround can be used to represent results of vector measurements in which there is statistical or other uncertainty.
• When VectorAround is used in computations, uncertainties are by default propagated using a first-order series approximation, taking account of correlations within each individual VectorAround object, but assuming no correlations between different VectorAround objects.
• Around[VectorAround[{x1,x2,},]] gives a list of Around[xi,] in which correlations between different values in the vector have been ignored.
• VectorAround[]["prop"] can be used to extract the following properties:
•  "Vector" central vector v in VectorAround[v,…] "Covariance" covariance matrix Δ "Correlation" correlation matrix R "Distribution"
• For linear computations, VectorAround[v,Δ] behaves like a vector whose values are distributed according to the multinormal distribution .
• VectorAround[{x1,x2},{{δ1,δ2},ρ}] gives VectorAround[{x1,x2},Δ], with covariance matrix Δ={{δ12,ρ δ1 δ2},{ρ δ1 δ2,δ22}}.
• For vectors v, δ and correlation matrix R, VectorAround[v,{δ,R}] gives VectorAround[v,Δ], with covariance matrix Δ of components Δij=Rij δi δj. The correlation matrix R is expected to have diagonal elements Rkk=1.

# Examples

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## Basic Examples(4)

A pair of uncorrelated uncertain numbers:

A pair of correlated uncertain numbers:

A pair of correlated quantities:

MeanAround on a list of vectors returns a VectorAround object:

## Properties & Relations(1)

Take a multinormal distribution for 2D vectors and simulate it:

VectorAround[vectors] estimates the mean and covariance matrix of the distribution:

MeanAround[vectors] describes the mean of the distribution and the covariance matrix associated with that mean: