In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...
85 KB (7,036 words) - 06:55, 11 May 2024
In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order...
25 KB (3,549 words) - 05:03, 24 April 2024
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a...
13 KB (1,906 words) - 14:52, 10 February 2024
the product of the Jones matrix of the optical element and the Jones vector of the incident light. Note that Jones calculus is only applicable to light...
28 KB (3,523 words) - 04:52, 4 February 2024
Orthonormalization of a set of vectors Irregular matrix Matrix calculus – Specialized notation for multivariable calculus Matrix function – Function that maps matrices...
105 KB (13,048 words) - 22:10, 26 May 2024
functions to a square matrix, extending what has just been discussed. In the finite-dimensional case, the polynomial functional calculus yields quite a bit...
4 KB (584 words) - 05:22, 2 February 2023
vector field Laplacian Laplacian vector field Level set Line integral Matrix calculus Mixed derivatives Monkey saddle Multiple integral Newtonian potential...
2 KB (156 words) - 12:13, 30 October 2023
inner-product space Matrix calculus, a specialized notation for multivariable calculus over spaces of matrices Numerical calculus (also called numerical...
5 KB (671 words) - 12:15, 17 May 2024
the Hessian matrix at these zeros. Vector calculus can also be generalized to other 3-manifolds and higher-dimensional spaces. Vector calculus is initially...
21 KB (2,078 words) - 17:06, 19 April 2024
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function...
21 KB (3,408 words) - 18:23, 27 December 2023
columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...
40 KB (6,456 words) - 13:03, 8 May 2024
integration Gabriel's horn Jacobian matrix Hessian matrix Curvature Green's theorem Divergence theorem Stokes' theorem Vector Calculus Infinite series Maclaurin...
4 KB (389 words) - 12:14, 10 February 2024
in the early 19th century. Calculus is composed of both inorganic (mineral) and organic (cellular and extracellular matrix) components. The mineral proportion...
33 KB (3,758 words) - 17:17, 28 May 2024
Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller...
10 KB (1,650 words) - 05:08, 5 July 2023
theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a...
43 KB (4,940 words) - 17:25, 24 March 2024
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...
19 KB (2,375 words) - 15:38, 29 April 2024
Jacobi's formula (category Matrix theory)
In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A....
10 KB (2,108 words) - 15:23, 29 May 2024
cross-vector. Dyadics Householder transformation Norm (mathematics) Ricci calculus Scatter matrix Cartesian product Cross product Exterior product Hadamard product...
18 KB (2,945 words) - 11:03, 23 February 2024
the derivatives of the rotated quaternion can be represented using matrix calculus notation as ∂ p ′ ∂ q ≡ [ ∂ p ′ ∂ q 0 , ∂ p ′ ∂ q x , ∂ p ′ ∂ q y ...
66 KB (11,513 words) - 13:31, 28 May 2024
Kronecker product (category Matrix theory)
Baksalary, Oskar Maria (2023). "Professor Heinz Neudecker and matrix differential calculus". Statistical Papers. doi:10.1007/s00362-023-01499-w. Langville...
40 KB (6,118 words) - 19:59, 25 April 2024
Trace (linear algebra) (redirect from Trace of a matrix)
same size. The Frobenius inner product and norm arise frequently in matrix calculus and statistics. The Frobenius inner product may be extended to a hermitian...
36 KB (5,364 words) - 15:13, 20 March 2024
called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns...
73 KB (8,575 words) - 02:33, 6 May 2024
Del (category Vector calculus)
or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol...
21 KB (3,846 words) - 05:41, 26 May 2024
especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector. Specifically...
10 KB (1,380 words) - 06:17, 7 October 2023
Transpose (redirect from Transpose of a matrix)
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
estimator can be performed via matrix calculus formulae (see also differential of a determinant and differential of the inverse matrix). It also verifies the...
25 KB (3,923 words) - 01:36, 24 August 2023
particular, T can be a square matrix with complex entries, a case which will be used to illustrate functional calculus and provide some heuristic insights...
31 KB (5,479 words) - 09:03, 7 November 2023
Derivative (redirect from Derivative (calculus))
The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input. The derivative...
55 KB (7,183 words) - 07:01, 15 May 2024
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each...
31 KB (4,873 words) - 16:47, 27 May 2024
formula Loewner order Matrix calculus Trace inequalities Trigonometric functions of matrices Higham, Nick (2020-12-15). "What Is the Matrix Sign Function?"...
12 KB (2,146 words) - 16:04, 13 January 2024