there exists an m × n {\displaystyle m\times n} matrix A {\displaystyle A} , called the transformation matrix of T {\displaystyle T} , such that: T ( x )...

dealt further in this article. Writing the general matrix transformation of coordinates as the matrix equation [ x ′ 0 x ′ 1 x ′ 2 x ′ 3 ] = [ Λ 0 0 Λ 0...

an affine transformation is invertible, the square matrix A {\displaystyle A} appearing in its matrix representation is invertible. The matrix representation...

&\lbrack b_{n}\rbrack _{C}\end{bmatrix}}} This matrix is referred to as the basis transformation matrix from B to C. It can be regarded as an automorphism...

elsewhere. The matrix A is said to represent the linear map f, and A is called the transformation matrix of f. For example, the 2×2 matrix A = [ a c b d...

applied mathematics, a DFT matrix is a square matrix as an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied...

transformation (named after Robert H. Park) is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix...

} A linear transformation L can be represented by a matrix, which means L : v → [L]v, where [L] is an n×n matrix. A linear transformation is a rigid transformation...

shear transformation, transvection, or just shearing. The transformations can be applied with a shear matrix or transvection, an elementary matrix that...

transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing...

Affine transformation, in geometry Linear transformation between modules in linear algebra. Also called a linear map. Transformation matrix which represent...

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

rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...

of a tridiagonal matrix is given by the continuant of its elements. An orthogonal transformation of a symmetric (or Hermitian) matrix to tridiagonal form...

Transformation geometry Transformation semigroup Transformation group Transformation matrix "Self-Map -- from Wolfram MathWorld". Retrieved March 4, 2024. Olexandr...

the form of an n by n matrix A, then the eigenvalue equation for a linear transformation above can be rewritten as the matrix multiplication A v = λ...

be defined by a nonsingular (n+1) × (n+1) matrix [ai,j], called the matrix of the homography. This matrix is defined up to the multiplication by a nonzero...

constant or multiplier of the transformation. The transformation is said to be elliptic if it can be represented by a matrix H {\displaystyle {\mathfrak...

example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous...

whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into...

its transformation matrix is first computed to transform the points, followed by multiplying the propeller model matrix by the aircraft's matrix for the...

Bogoliubov transformations are linear recombination of operators, it is more convenient and insightful to write them in terms of matrix transformations. If a...

Such a matrix is also called a Frobenius matrix, a Gauss matrix, or a Gauss transformation matrix. A block triangular matrix is a block matrix (partitioned...

Though matrix representations are not strictly necessary for Galilean transformation, they provide the means for direct comparison to transformation methods...

being the change-of-basis matrix. A transformation A ↦ P−1AP is called a similarity transformation or conjugation of the matrix A. In the general linear...

contravariant transformations, with one transformation law for each index. If the transformation matrix of an index is the inverse matrix of the basis...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

.} An n × n matrix M can represent a linear map and act on row and column vectors as the linear map's transformation matrix. For a row vector v...

numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix preserves the inner product of vectors...

the Hunt–Pointer–Estevez transformation matrix (MHPE) for conversion from CIE XYZ to LMS. This is the transformation matrix which was originally used...