According to Algebra, a determinant basically is a task depending on n that associates a scalar, det(A), to every n×n square matrix A. The basic geometric meaning of a determinant is as the scale factor for volume when A is thought of as a linear transformation.
Determinants are generally essential in both calculi, where they enter the substitution rule for many variables and also in multi linear algebra. For a set positive integer n, there is an exclusive determinant meaning for the n×n matrix over any commutative ring R.
Predominantly this meaning is there when R is the field of real or compound numbers. A determinant of A is even at times indicated by |A|, but this notion is ambiguous. It is even applied for particular matrix norms and even for absolute value.
Determinants are generally essential in both calculi, where they enter the substitution rule for many variables and also in multi linear algebra. For a set positive integer n, there is an exclusive determinant meaning for the n×n matrix over any commutative ring R.
Predominantly this meaning is there when R is the field of real or compound numbers. A determinant of A is even at times indicated by |A|, but this notion is ambiguous. It is even applied for particular matrix norms and even for absolute value.
