# 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.
References in periodicals archive ?
The method employs the global similarity transformation with the combination of local hommography.
The algorithm in [21, 28] is based on introducing a similarity transformation T that transforms the general linear system in implicit singularly perturbed form into the explicit singularly perturbed form defined in (9).
Each iteration consists of three steps: choose a suitable shift to enhance the convergence, apply a similarity transformation to create a bulge, and chase the bulge until it disappears from the bottom of the matrix.
Therefore, in this paper, similarity transformation methods are used to access instances before manual screening, which helps improve the efficiency of instance access greatly.
Verma and Mishra [4] have obtained solution by similarity transformation of one-dimensional vertical ground water recharges through porous media.
Invariants of Geometric Moments under Similarity Transformation
By applying the same similarity transformation as the designed one to the matrix [[M.
They developed a similarity transformation method in which the boundary layer equation was reduced to a third-order nonlinear ordinary differential equation.
Here the solution is obtained by regarding cross-sectional velocity as perturbation parameter that has been solved by using similarity transformation and singular perturbation technique.
The hydrodynamics of the thin liquid film over a stretching sheet were first considered by Wang [17] who reduced the unsteady Navier-Stokes equations to the coupled nonlinear ordinary differential equations by similarity transformation and solved the problem using a kind of multiple shooting method (see Roberts and Shipman [18]).
These rotations are then brought by a similarity transformation back to the left-hand side.
To complete the similarity transformation, we must apply this block transform from the left and from the right to A.

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