We introduce singular subalgebroids of an integrable Lie algebroid, extending the notion subalgebroid by dropping constant rank requirement. lay bases a theory for subalgebroids: we construct associated holonomy groupoids, adapting procedure Androulidakis-Skandalis foliations, in way that keeps track choice groupoid integrating ambient algebroid. The groupoids are topological and suitable nonco...

Let A 2 R mn be a matrix with known singular values and singular vectors, and let A 0 be the matrix obtained by appending a row to A. We present stable and fast algorithms for computing the singular values and the singular vectors of A 0 in O ? (m + n) min(m;n) log 2 2 oating point operations, where is the machine precision. Previous algorithms can be unstable and compute the singular values an...

We study (i-)locally singular hyperplanes in a thick dual polar space of rank n. If is not of type DQ(2n,K), then we will show that every locally singular hyperplane of is singular. We will describe a new type of hyperplane in DQ(8,K) and show that every locally singular hyperplane of DQ(8,K) is either singular, the extension of a hexagonal hyperplane in a hex or of the new type. © 2005 Elsevie...