Determinant

In linear algebra, a determinant is a function depending on n that associates a scalar det(A) to every n×n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor for volume when A is regarded as a linear transformation. Determinants are important both in calculus, where they enter the substitution rule for several variables, and in multilinear algebra.

Related Topics:
Linear algebra - Function - Scalar - Square matrix - Scale factor - Volume - Linear transformation - Calculus - Substitution rule - Multilinear algebra

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For a fixed positive integer n, there is a unique determinant function for the n×n matrices over any commutative ring R. In particular, this is true when R is the field of real or complex numbers.

Related Topics:
Field - Real - Complex number

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A determinant of A is also sometimes denoted by |A|, but this notation is ambiguous: it is also used to for certain matrix norms, and for the square root of {AA}^*.

Related Topics:
Matrix norm - Square root

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