We present an algorithm for computing a d-dimensional subspace of the row space of a matrix. For an n×n matrix A with m nonzero entries and with rank(A) ≥ d the algorithm generates a d × n matrix with full row rank and which is a subspace of Rows(A). If rank(A) < d the algorithm generates a rank(A)×n row-equivalent matrix. The running time of the algorithm is

Necessary and sufficient conditions for the existence of at least a full-column rank solution to the matrix equation AV 1⁄4 EVJ is obtained when the matrix pair ðA;EÞ is regular. Furthermore, a simple representation of the all full-column rank solutions to the matrix equation is derived if it has such solutions. An example illustrates the proposed approach. 2003 Elsevier Inc. All rights reserved.

Conditions are presented for different types of identifiability of discrete variable models generated over an undirected graph in which one node represents a binary hidden variable. These models can be seen as extensions of the latent class model to allow for conditional associations between the observable random variables. Since local identification corresponds to full rank of the parametrizat...

Mobile devices have fewer antennas than APs due to size and energy constraints. This antenna asymmetry restricts uplink capacity to the client antenna array size rather than the AP’s. To overcome antenna asymmetry, multiple clients can be grouped into a simultaneous multiuser transmission to achieve a full rank transmission that matches the number of antennas at the AP. In this paper, we design...

Optimal multi-antenna wide-band signaling schemes are derived for multipath channels assuming perfect channel state information at the transmitter. The scheme that minimizes the biterror probability in the single-user case is a rank-one space–time beamformer which focuses the signal transmission in the direction of the most dominant channel mode. Several suboptimal variations are discussed for ...

Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain circumstances, namely when the covariance matrix of the nonlinearly expanded data does not have full rank, this implementation runs into numerical instabilities. We pro...

In all books and papers on adaptive filtering, the input autocorrelation matrix Rxx is always considered positive definite and hence the theoretical Wiener–Hopf normal equations (Rxxh 1⁄4 rxd) have a unique solution h 1⁄4 hopt (‘‘there is only a single global optimum’’, [B. Widrow, S. Stearns, Adaptive Signal Processing, Prentice-Hall, 1985, p. 21]) due to the invertibility of Rxx (i.e., it is ...