Similarity transformation may refer to: Similarity (geometry), for shape-preserving transformations Matrix similarity, for matrix transformations of the...

ratio of similarity, the stretching factor and the similarity coefficient. When r = 1 a similarity is called an isometry (rigid transformation). Two sets...

matrix. A transformation A ↦ P−1AP is called a similarity transformation or conjugation of the matrix A. In the general linear group, similarity is therefore...

conformal linear transformation, also called a homogeneous similarity transformation or homogeneous similitude, is a similarity transformation of a Euclidean...

turbulent flow in wind tunnels with smaller-scale models. Similarity transformations (also called similarity laws) help us work out how plasma properties change...

to appreciate the self-similarity of these fractal objects, they have to be rescaled using an anisotropic affine transformation. A compact topological...

analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of...

datum transformations between datums. The Helmert transformation is also called a seven-parameter transformation and is a similarity transformation. It...

but not every affine transformation is linear. Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation...

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that...

assessments of similarity. Structural approaches to similarity emerged from research on analogy. Transformational accounts of similarity (Hahn, Chater...

of basis matrix of the similarity transformation. Essentially, the matrices A and Λ represent the same linear transformation expressed in two different...

tridiagonal matrices one can compute the eigendecomposition using a similarity transformation. Given a real tridiagonal, nonsymmetric matrix T = ( a 1 b 1 c...

unitary similarity transformation of these subalgebras will yield SU(2) subalgebras. There is an uncountable number of such transformations. The 8 generators...

to g. In projective geometry, a homothetic transformation is a similarity transformation (i.e., fixes a given elliptic involution) that leaves the line...

algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection...

Any invertible matrix P {\displaystyle \mathbf {P} } defines a similarity transformation (on square matrices of the same size as P {\displaystyle \mathbf...

simultaneous diagonalization is not necessarily performed with a similarity transformation. This result does not extend to the case of three or more matrices...

previous section. The Jordan normal form is obtained by some similarity transformation: P − 1 A P = J ; {\displaystyle P^{-1}AP=J;} that is, A P = P...

precisely equivariant) under similarity transformations. In other words, for any triangle and any similarity transformation (such as a rotation, reflection...

More generally, all triangle centers are also equivariant under similarity transformations (combinations of translation, rotation, reflection, and scaling)...

composition of translations, similarities, orthogonal transformations and inversions. The general form of a Möbius transformation is given by f ( z ) = a z...

invertible matrix P {\displaystyle P} . In other words, if there is a similarity transformation: D ′ ( a ) ≡ P − 1 D ( a ) P , {\displaystyle D'(a)\equiv P^{-1}D(a)P...

Hessenberg matrix by a similarity transformation using Householder transformations. The following procedure for such a transformation is adapted from A Second...

therefore A {\displaystyle A} may not be diagonalized by any similarity transformation.) Using the Jordan normal form, one can prove that every square...

In linear algebra, similarity invariance is a property exhibited by a function whose value is unchanged under similarities of its domain. That is, f {\displaystyle...

Coordinate rotations and reflections Translation Glide reflection Similarity Similarity transformation Homothety Shear mapping 2D computer graphics 2D geometric...

A} as columns in M {\displaystyle M} . It is utilized in the similarity transformation D = M − 1 A M , {\displaystyle D=M^{-1}AM,} where D {\displaystyle...

normal matrices can be brought to diagonal form by a unitary similarity transformation: A U = U diag ⁡ ( α 1 , … , α m ) ⟺ U † A U = diag ⁡ ( α 1 , …...

M} such that A {\displaystyle A} is diagonalizable through the similarity transformation D = M − 1 A M {\displaystyle D=M^{-1}AM} . The matrix D {\displaystyle...