(a) Another Orthogonal Matrix & (b) An application of Pfaff's Theorem (on skew-symmetric matrices)

Abstract 1 Another Orthogonal Matrix

A householder reflection and a suitable product of Givens rotations are two well known examples of an orthogonal matrix with given first column. We present another way to produce such a matrix and apply it to produce a "fast Givens" method to compute the R factor of A, A = QR. This approach avoids the danger of under/overflow.
(joint work with Eric Barszcz)

Abstract 2 An application of Pfaff's Theorem (on skew-symmetric matrices)

There are no constraints on the eigenvalues of a product of two real symmetric matrices but what about the product of two real skew-symmetric matrices?
(joint work with A Dubrulle)