Index Matrices: Definitions, Operations, Relations - Index Matrices: Towards an Augmented Matrix Calculus - page 13

∧

-column-aggregation

l 0

k 1 ∧ a k 1 , l j

1 ≤ j ≤ n

σ ∧ ( A , l 0 ) = ,

. .

k m ∧ a k m , l j

1 ≤ j ≤ n

Now, let us give some examples. Let α,...,ϕ be, e.g., some logical variables.

Let the following L-IMs A , B , C , D , E be given

cde cq

a αβγ a κλ

A = B =

b δεζ p μν

e ηθι e ξ o

cqe q

cqe

a κλμ c τ

C = a κλμ D = E =

p νξ o d υ

p νξ o

e πρσ p ϕ

Then, we can construct the following new IMs:

c d e q

a α ∨ κβ γ λ

A ⊕ ∨ B = b δ ε ζ false

e η ∨ ξθ ι o

p μ false false ν

c d e q

a α ∧ κβγ ∧ μλ

A ⊕ ∧ C = b δ ε ζ false

e η θ ι false

p ν false o ξ

c d e q

a α → κβγ → μλ

A ⊕ → D = δ ε ζ

b false

η → πθ ι → σρ

e

p ν false o ξ