The Cayley transform of prevalent matrix classes

The Cayley transform of a matrix A, C(A) = (I+A)-1(I-A), has been investigated in the contexts of skew-symmetry, eigen-value mapping and as a factorization technique for several matrix positivity classes. Here, we extend the discussion to Cayley transforms of almost skew-Hermitian matrices, posi-tive definite matrices, semipositive matrices, as well as sub-classes of the M-matrices, H-matrices and their inverses. (c) 2023 Elsevier Inc. All rights reserved.