Condition by Peter Bürgisser & Felipe Cucker

Author:Peter Bürgisser & Felipe Cucker
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

By this lemma, Dπ(M) provides an isomorphism of the orthogonal complement of with the tangent space T π(M) Y of Y at . In the following, we shall identify T π(M) Y with this subspace of T M St n,k to have a concrete model to work with. This also defines a Riemannian metric on Y.

The following result shows that κ(A)=∥A∥ acond G (A), and hence κ(A) can be interpreted as the relative condition number for computing the kernel of A from a given A.

Proposition 14.19

We have acond G (A)=∥A †∥ for A∈X.

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