Interval Analysis

3Interval vectors, interval matrices

3.1Basics

Interval vectors and interval matrices are defined as vectors and matrices with interval entries. Thus

is a real interval (column) vector with n components [x]_i ∈ 𝕀ℝ, i = 1, …, n, and

is a real m × n interval matrix with entries [a]_ij ∈ 𝕀ℝ, i = 1, …, m, j = 1, …, n. The set of all real interval vectors with n components is denoted by 𝕀ℝⁿ, that of all real m × n interval matrices by 𝕀ℝ^m×n. Analogously to Chapter 2 we use the notation 𝕀(S) for S ⊆ ℝⁿ or S ⊆ ℝ^{m × n}.

We call n and m × n the dimension of ...