Matrices with prescribed eigenvalues and prescribed submatrices

Some matrix completion problems

“…3 ×p 2 such that the matrix of the form (2) has characteristic polynomial f . Now consider the following conditions: (2) has characteristic polynomial f if and only if either (i 2.1 ) or (ii 2.1 ) is satisfied.…”

“…that the matrix of the form (2) has characteristic polynomial f if and only if there exists A 1,3 ∈ F p 1 ×p 3 , A 2,1 ∈ F p 2 ×p 1 ,…”

“…Then there exists A 1,3 ∈ F p 1 ×p 3 , A 2,1 ∈ F p 2 ×p 1 , A 2,2 ∈ F p 2 ×p 2 , A 3,1 ∈ F p 3 ×p 1 , A 3,2 ∈ F p 3 ×p 2 , A 3,3 ∈ F p 3 ×p 3 such that the matrix of the form (2) has characteristic polynomial f if and only if α 1 · · · α p 1 −p 3 |f.…”