7 articles
Hessian matrix
The Hessian matrix, or Hesse matrix, is the square matrix of a function's second-order partial derivatives, used to classify critical points as minima, maxima, or saddle points.
Jacobi's formula
Jacobi's formula is a theorem of matrix calculus stating that the differential of a square matrix's determinant equals the trace of its adjugate times the matrix differential.
Matrix calculus
Matrix calculus, also called matrix differentiation, extends differential calculus to functions whose arguments or values are vectors or matrices, and is central to statistics, econometrics, and machine learning.
Matrix exponential
The matrix exponential, or exponential of a matrix, generalizes the scalar exponential to square matrices via a convergent power series and gives the closed-form solution of linear differential systems.
Matrix function
A matrix function extends a scalar function such as the exponential, logarithm, sine, or square root to a square matrix, defined through the matrix's eigenstructure rather than applied to each entry.
Matrix logarithm
The matrix logarithm of a square matrix A is any matrix X whose matrix exponential is A, so e^X = A. It need not exist or be unique.
Vectorization (mathematics)
Vectorization, written vec, is the linear-algebra operation that stacks a matrix's columns into a single column vector, connecting matrix algebra to ordinary vector calculus.