ABSTRACT
This section gives a short outline on linear independence of (column and row, respectively) vectors ( k i ∈ ℜ ν $ (k_{i} \in {\Re }^{\nu } $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432286/e5317931-e1ce-444d-956f-32e255527c7d/content/inline-math7_1.tif"/> and c i ∈ C ν , i = 1 , 2 , … , μ , r j ∈ ℜ 1 × μ $ c_{i} \in C^{\nu } ,i = 1,2, \ldots ,\mu ,r_{j} \in {\Re }^{1 \times \mu } $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432286/e5317931-e1ce-444d-956f-32e255527c7d/content/inline-math7_2.tif"/> and z j ∈ C 1 × μ , j = 1 , 2 , … , ν ) . $ z_{j} \in {\mathbb{C}}^{1 \times \mu } ,j = 1,2, \ldots ,\nu ). $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432286/e5317931-e1ce-444d-956f-32e255527c7d/content/inline-math7_3.tif"/> The brief reminder of the linear (in)dependence and of the rank of the matrices is helpful to emphasize the subtle but crucial differences between the matrices and matrix functions.
