Chapter 27

Generalized Inverses of Matrices

Yimin Wei

Fudan University

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 AFm × n, and let bFm.

For integers m ≥ 1 and 1 ≤ km,

Qk,m={α:α=(α1,α2,...,αk),1α1<α2<<αkm, and α1,α2,...,αk are integers}.

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 ...

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