1 Linear algebra 2 1.1 Inner product, norm, distance, and orthogonality . . . . . . . . . 2 1.2 Angle and inequality . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Vector projection . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Basics of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . ....

We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicity-free decomposition i...

Suppose E/F is a quadratic extension of number fields and GU(2, 2) is the quasi-split unitary similitude group attached to E/F . We prove functoriality from globally generic cuspidal representations of GU(2, 2)(AF ) to automorphic representations of GL6(AF ) corresponding to the twisted exterior square map on the dual side. For a split quadratic algebra E/F , the twisted exterior square map red...

A parallel algorithm for transforming an n × n symmetric matrix to tridiagonal form is described. The algorithm implements Givens rotations on a square array of n × n processors in such a way that the transformation can be performed in time O(n log n). The processors require only nearest-neighbor communication. The reduction to tridiagonal form could be the first step in the parallel solution o...

This paper introduces balanced switching schemes to compensate linear and quadratic gradient errors, in the unary current source array of a current-steering digital-to-analog converter (DAC). A novel algorithm is proposed to avoid the accumulation of gradient errors, yielding much less integral nonlinearities (INLs) than conventional switching schemes. Switching scheme examples with different n...