Generalized Inverses of Matrices
Throughout this chapter, we will survey some basic results on the Moore-Penrose inverse, the Drazin inverse, and the outer inverse.
27.1 Notation and Terminology
Let F be a field (usually ℂ or ℝ), let A ∈ Fm × n, and let b ∈ Fm.
For integers m ≥ 1 and 1 ≤ k ≤ m,
For α ∈ Qk,m and β ∈ Ql,n, the submatrix A[α, β] is the k × l matrix whose (i, j)-th element is the (αi, βj) element of A; see Chapter 11 for additional information about submatrices. If |β| = n (or |α| = m), then the notation A[α, *] (or A[*, β] = A[α, β]) is used to denote A[α, β].
For α ∈ Qk, m, b[α] is the subvector of b, whose ...