Normalized Frobenius condition number of the orthogonal projections of the identity

作者：Suarez Antonio; Gonzalez Luis^*

来源：Journal of Mathematical Analysis and Applications, 2013, 400(2): 510-516.

DOI：10.1016/j.jmaa.2012.11.021

• Frobenius norm minimization
• Orthogonal projections
• Frobenius condition number

This paper deals with the orthogonal projection (in the Frobenius sense) AN of the identity matrix I onto the matrix subspace AS (A is an element of R-nxn, S being an arbitrary subspace of R-nxn). Lower and upper bounds on the normalized Frobenius condition number of matrix AN are given. Furthermore, for every matrix subspace S subset of R-nxn, a new index (kappa) over cap (F) (A, S), which generalizes the normalized Frobenius condition number of matrix A, is defined and analyzed.

• 出版日期2013-4-15