Abstract
This paper deals with the orthogonal projection (in the Frobenius sense) AN of the identity matrix I onto the matrix subspace AS (A∈Rn×n, S being an arbitrary subspace of Rn×n). Lower and upper bounds on the normalized Frobenius condition number of matrix AN are given. Furthermore, for every matrix subspace S⊂Rn×n, a new index κ̂F(A,S), which generalizes the normalized Frobenius condition number of matrix A, is defined and analyzed.
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