It has to be passed through the upper triangular matrix first and next a unitary
similarity transformation eliminates the triangle on the right and reintroduces it on the left.
Hiemenz [3] studied the steady two-dimensional boundary layer flows near the forward stagnation point on an infinite wall using a
similarity transformation. Sakiadis [4, 5] reported the flow field analysis where the stretched surface was assumed to move with uniform velocity, and similarity solutions were obtained for the governing equations.
A set of invariants are derived from Zernike moments which are simultaneously invariant to
similarity transformation and to convolution with circularly symmetric PSF [17].
To complete the
similarity transformation, the transposed Givens transformation has to be applied to the columns; see Figure 4.4(c).
Integrability conditions on (1) for exact solutions by the
similarity transformation used in the paper are
Therefore, for each !, the derivatives of the nodes [[lambda].sub.1], ..., [[lambda].sub.K] are easily obtained by applying a
similarity transformation to the matrix of the derivatives of the recursion coefficients, [T'.sub.[omega]](0), where the transformation involves a matrix, [Q.sub.[omega]](0), that must be computed anyway to obtain the weights.
Hence, the first step of the implicit SR step introduces a bulge by a
similarity transformation of H with
First we transform A to an upper Hessenberg matrix H = [V.sup.*] AV by a unitary
similarity transformation. Then we balance the Hessenberg matrix before computing its eigenvalues.
[9] Every skew-Hamiltonian matrix is similar, via an orthogonal symplectic
similarity transformation, to a matrix in skew-Hamiltonian Schur form.
THE RELATION WITH THE HELMERT
SIMILARITY TRANSFORMATIONIn Section 2 we present the Schwarzian derivative {z, x} and the invariant I(z) of the differential equation [u.sub.zz] + f(z)[u.sub.z] + g(z)u = 0 through acting the
similarity transformation [psi](z) = [phi](z)u(z) on the Schrodinger equation.
The two canonical forms are related by a
similarity transformation coupled with a redefinition of the time variable.