VectorAround [{x₁,x₂,…},{δ₁,δ₂,…}]

represents a vector of uncorrelated approximate numbers or quantities with values x_i and uncertainties δ_i.

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

represents a vector of approximate numbers or quantities with values x_i 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 δ_i and correlation matrix R.

• 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 [x_i,…] 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" MultinormalDistribution […]
• For linear computations, VectorAround [v,Δ] behaves like a vector whose values are distributed according to the multinormal distribution MultinormalDistribution [v,Δ].
• 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 Δ_ij=R_ij δ_i δ_j. The correlation matrix R is expected to have diagonal elements R_kk=1.

Basic Examples  (4)

Properties & Relations  (1)