} for some m × n {\displaystyle m\times n} matrix A {\displaystyle A} , called the transformation matrix of T {\displaystyle T} .[citation needed] Note...
24 KB (3,826 words) - 19:39, 10 March 2024
an affine transformation is invertible, the square matrix A {\displaystyle A} appearing in its matrix representation is invertible. The matrix representation...
27 KB (3,594 words) - 20:28, 28 March 2024
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...
103 KB (14,094 words) - 09:31, 6 May 2024
Coordinate vector (redirect from Basis transformation matrix)
&\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...
8 KB (1,310 words) - 04:38, 4 February 2024
conjugate transpose v * {\textstyle v^{\textsf {*}}} . The matrix constructed from this transformation can be expressed in terms of an outer product as: P =...
15 KB (2,267 words) - 04:26, 22 May 2024
example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous...
6 KB (841 words) - 00:48, 13 August 2023
Shear mapping (redirect from Shear transformation)
shear transformation, transvection, or just shearing. The transformations can be applied with a shear matrix or transvection, an elementary matrix that...
13 KB (1,885 words) - 13:26, 3 May 2024
Similarity transformation may refer to: Similarity (geometry), for shape-preserving transformations Matrix similarity, for matrix transformations of the form...
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a DFT matrix is an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied to a signal through matrix multiplication...
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square matrix are the roots of a polynomial determinant. In geometry, matrices are widely used for specifying and representing geometric transformations (for...
106 KB (13,106 words) - 20:37, 21 May 2024
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...
8 KB (1,081 words) - 22:27, 10 April 2024
} 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...
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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 = [...
99 KB (15,019 words) - 04:42, 13 May 2024
of a tridiagonal matrix is given by the continuant of its elements. An orthogonal transformation of a symmetric (or Hermitian) matrix to tridiagonal form...
15 KB (2,252 words) - 17:44, 24 February 2024
Bogoliubov transformations are linear recombination of operators, it is more convenient and insightful to write them in terms of matrix transformations. If a...
14 KB (1,896 words) - 09:41, 19 April 2024
Eigenvalues and eigenvectors (redirect from Eigenvalue (Matrix))
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...
101 KB (13,539 words) - 03:39, 8 April 2024
component). The power-invariant, right-handed, uniformly-scaled Clarke transformation matrix is K C = 2 3 ⋅ [ 1 − 1 2 − 1 2 0 3 2 − 3 2 1 2 1 2 1 2 ] {\displaystyle...
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Affine transformation, in geometry Linear transformation between modules in linear algebra. Also called a linear map. Transformation matrix which represent...
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Tensor (redirect from Tensor transformation law)
contravariant transformations, with one transformation law for each index. If the transformation matrix of an index is the inverse matrix of the basis...
69 KB (9,356 words) - 22:51, 9 May 2024
whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into...
7 KB (802 words) - 01:33, 4 January 2024
Transpose (redirect from Transpose of a linear transformation)
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...
20 KB (2,525 words) - 12:30, 8 May 2024
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...
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Homography (redirect from Projective transformation matrix)
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...
30 KB (3,641 words) - 01:24, 25 February 2024
Though matrix representations are not strictly necessary for Galilean transformation, they provide the means for direct comparison to transformation methods...
17 KB (2,572 words) - 15:35, 14 July 2023
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...
17 KB (2,466 words) - 02:48, 13 May 2024
constant or multiplier of the transformation. The transformation is said to be elliptic if it can be represented by a matrix H {\displaystyle {\mathfrak...
70 KB (10,549 words) - 17:06, 7 May 2024
vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial...
25 KB (3,549 words) - 05:03, 24 April 2024
Forward kinematics (section Denavit-Hartenberg matrix)
1 T i ( θ i ) {\displaystyle {}^{i-1}T_{i}(\theta _{i})} is the transformation matrix from the frame of link i {\displaystyle i} to link i − 1 {\displaystyle...
8 KB (1,310 words) - 16:51, 26 April 2024
Determinant (redirect from Matrix determinant)
square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the...
89 KB (14,131 words) - 05:28, 17 May 2024
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...
21 KB (3,152 words) - 16:41, 28 April 2024