Li, Bingxiang; Li, Wen; Cui, Lubin New bounds for perturbation of the orthogonal projection. (English) Zbl 1266.65064 Calcolo 50, No. 1, 69-78 (2013). For a matrix \(M\) with Moore-Penrose inverse \(M^†\), define the projection matrix \(P_M=MM^†\). Consider a matrix \(A\) and its perturbation \(B\) that can be additive (\(B=A+E\)) or multiplicative (\(B=D_1AD_2\)) then this paper gives a bound for \(\|P_A-P_B\|\) for a general unitarily invariant norm. The analysis is based on the singular value decomposition of the matrix \(A\) and is a slight improvement over known estimates. The disadvantage is however that the bounds not only assume some knowledge of the perturbing matrices and the singular values of \(A\) but they also involve the singular vectors. Reviewer: Adhemar Bultheel (Leuven) Cited in 4 Documents MSC: 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65F10 Iterative numerical methods for linear systems Keywords:singular value decomposition; orthogonal projection; additive perturbation; multiplicative perturbation; Moore-Penrose inverse PDFBibTeX XMLCite \textit{B. Li} et al., Calcolo 50, No. 1, 69--78 (2013; Zbl 1266.65064) Full Text: DOI References: [1] Bhatia, R.: Matrix Analysis. Springer, New York (1997) · Zbl 0863.15001 [2] Chen, X.S., Li, W.: Relative perturbation bounds for the subunitary polar factor under unitarily invariant norms. Adv. Math. 35, 178–184 (2006) (in Chinese) [3] Li, W.: Some new perturbation bounds for subunitary polar factors. Acta Math. Sinica (Eng. Ser) 21(6), 1515–1520 (2005) · Zbl 1101.65041 · doi:10.1007/s10114-004-0478-0 [4] Stewart, G.W.: On the perturbation of the pseudo-inverse, projections and linear squares problems. SIAM Rev. 19, 634–662 (1977) · Zbl 0379.65021 · doi:10.1137/1019104 [5] Sun, J.: Matrix Perturbation Analysis, 2nd edn. Science Press, Beijing (2001) (in Chinese) · Zbl 1013.15004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.