Geodesic
Congruences and Norms of Hermitian Matrices
Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1446-1458

Voir la notice de l'article provenant de la source Cambridge University Press

Two complex hermitian n × n matrices A and B are congruent if S*AS = B for some invertible n × n matrix S (with complex entries). The matrix S is called a congruence matrix. Given congruent hermitian matrices A and B, a congruence matrix is, of course, not unique. For instance, if A = B then one can take S = αI with |α| = 1, as well as any other matrix satisfying S*AS = A. However, here the choice S = I seems naturally to be best possible in the sense that when applied to an n-dimensional column vector it produces no distortion or movement of the vector at all. We shall measure the distortion (or movement) of the vector x ∊ C n under an n × n invertible matrix A in terms of ║x − Ax║, where the norm is euclidean. Then the distortion produced by A is ║I − A║, with the induced operator norm. 
Pierce, Stephen; Rodman, Leiba. Congruences and Norms of Hermitian Matrices. Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1446-1458. doi: 10.4153/CJM-1987-068-9
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[1] 1. Campbell, S. L. and Meyer, C. D. Jr., Generalized inverses of linear transformations, (Pitman, London, etc., 1979). Google Scholar

[2] 2. Gohberg, I. and Rodman, L., Perturbations of lattices of invariant subspaces of matrices, Lin. Alg. and Appl. 76 (1985), 85–120. Google Scholar

[3] 3. Gohberg, I., Lancaster, P. and Rodman, L., Invariant subspaces of matrices with applications, (J. Wiley, 1986). Google Scholar

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