In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...

In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a...

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...

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...

Orthonormalization of a set of vectors Irregular matrix Matrix calculus – Specialized notation for multivariable calculus Matrix function – Function that maps matrices...

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...

inner-product space Matrix calculus, a specialized notation for multivariable calculus over spaces of matrices Numerical calculus (also called numerical...

functions to a square matrix, extending what has just been discussed. In the finite-dimensional case, the polynomial functional calculus yields quite a bit...

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...

vector field Laplacian Laplacian vector field Level set Line integral Matrix calculus Mixed derivatives Monkey saddle Multiple integral Newtonian potential...

the Hessian matrix at these zeros. Vector calculus can also be generalized to other 3-manifolds and higher-dimensional spaces. Vector calculus is initially...

integration Gabriel's horn Jacobian matrix Hessian matrix Curvature Green's theorem Divergence theorem Stokes' theorem Vector Calculus Infinite series Maclaurin...

in the early 19th century. Calculus is composed of both inorganic (mineral) and organic (cellular and extracellular matrix) components. The mineral proportion...

Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller...

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...

cross-vector. Dyadics Householder transformation Norm (mathematics) Ricci calculus Scatter matrix Cartesian product Cross product Exterior product Hadamard product...

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....

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a...

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...

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...

Baksalary, Oskar Maria (2023). "Professor Heinz Neudecker and matrix differential calculus". Statistical Papers. doi:10.1007/s00362-023-01499-w. Langville...

called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns...

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 ...

especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector. Specifically...

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...

or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol...

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...

estimator can be performed via matrix calculus formulae (see also differential of a determinant and differential of the inverse matrix). It also verifies the...

mixed state ρ. Matrix function Holomorphic functional calculus Logarithm of a matrix Sylvester's formula Square root of a 2 by 2 matrix Higham, Nicholas...

formula Loewner order Matrix calculus Trace inequalities Trigonometric functions of matrices Higham, Nick (2020-12-15). "What Is the Matrix Sign Function?"...