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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, ...
A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries. Matrices have a long history of both study and application, leading to diverse ways of classifying matrices. A first group is matrices satisfying concrete conditions of the entries, including constant matrices.
In particular, elementary row operations correspond to elementary matrices. This fact can be seen as an instance of the Yoneda lemma for the category of matrices. [4] [5] The transpose operation makes the category of matrices a dagger category. The same can be said about the conjugate transpose in the case of complex numbers.
The n × n matrices that have an inverse form a group under matrix multiplication, the subgroups of which are called matrix groups. Many classical groups (including all finite groups) are isomorphic to matrix groups; this is the starting point of the theory of group representations. Matrices are the morphisms of a category, the category of ...
In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector , where is the row vector transpose of . [1] More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector , where denotes the ...
C. Cabibbo–Kobayashi–Maskawa matrix; Cartan matrix; Cauchy matrix; Centering matrix; Central groupoid; Centrosymmetric matrix; Circulant matrix; Column groups and row groups
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.
The elementary matrices generate the general linear group GL n (F) when F is a field. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations.