similarity transformation


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similarity transformation

[‚sim·ə′lar·əd·ē ‚tranz·fər‚mā·shən]
(mathematics)
A transformation of a euclidean space obtained from such transformations as translations, rotations, and those which either shrink or expand the length of vectors.
A mapping that associates with each linear transformation P on a vector space the linear transformation R -1 PR that results when the coordinates of the space are subjected to a nonsingular linear transformation R.
A mapping that associates with each square matrix P the matrix Q = R -1 PR, where R is a nonsingular matrix and R -1 is the inverse matrix of R ; if P is the matrix representation of a linear transformation, then this definition is equivalent to the second definition.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
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.
In 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.