where both U and A are unitary matrices
and [SIGMA] is a diagonal matrix.
To derive a structure preserving deflation under unitary structure preserving transformations, consider the unitary matrices
U, V obtained in (2.
N]] (having dimensions Q x Q and N x N) are left and right unitary matrices
Let U(N) denote the group of all N x N unitary matrices
Matrices [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are unitary matrices
and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the unitary matrices
of i-mode singular vectors for i = 1, 2, 3.
Yayli, Dual unitary matrices
and unit dual quaternions, Differential Geometry Dynamical Systems, 10(2008), 1-12.
U and V are real N x N unitary matrices
with small singular values.
Note that the technique used in the proof above can be extended easily to handle bigger input alphabets by using the matrices defined on Page 169 of [Paz71], and the method of simulating stochastic matrices by unitary matrices
described in [YS09b, YS10].
This third edition features new chapters on generalized eigenvectors and numerical techniques, as well as a new section on Hermitian symmetric and unitary matrices
Y], they have group operations represented by 2 x 2 unitary matrices
or, equivalently, by unit quaternions.