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  2. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.

  3. Kronecker product - Wikipedia

    en.wikipedia.org/wiki/Kronecker_product

    In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis.

  4. List of formal systems - Wikipedia

    en.wikipedia.org/wiki/List_of_formal_systems

    Matrix calculus, a specialized notation for multivariable calculus over spaces of matrices Umbral calculus , the combinatorics of certain operations on polynomials Vector calculus (also called vector analysis), comprising specialized notations for multivariable analysis of vectors in an inner-product space

  5. Matrix (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Matrix_(mathematics)

    In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

  6. Jacobi's formula - Wikipedia

    en.wikipedia.org/wiki/Jacobi's_formula

    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. [1]If A is a differentiable map from the real numbers to n × n matrices, then

  7. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    Toggle the table of contents. Matrix multiplication. 35 languages. ... Matrix calculus, for the interaction of matrix multiplication with operations from calculus;

  8. Category of matrices - Wikipedia

    en.wikipedia.org/wiki/Category_of_matrices

    A stochastic matrix is a real matrix of nonnegative entries, such that the sum of each column is one. Stochastic matrices include the identity and are closed under composition, and so they form a subcategory of M a t R {\displaystyle \mathbf {Mat} _{\mathbb {R} }} .

  9. Proofs involving ordinary least squares - Wikipedia

    en.wikipedia.org/wiki/Proofs_involving_ordinary...

    Using matrix notation, the sum of squared residuals is given by S ( β ) = ( y − X β ) T ( y − X β ) . {\displaystyle S(\beta )=(y-X\beta )^{T}(y-X\beta ).} Since this is a quadratic expression, the vector which gives the global minimum may be found via matrix calculus by differentiating with respect to the vector β {\displaystyle \beta ...