Changes

The '''determinant''' of a [[matrix]] (written |A|) is a single number that depends on the elements of the matrix A. Determinants exist only for square matrices (i.e., ones where the number of rows equals the number of columns).  

The '''determinant''' of a [[matrix]] (written |A|) is a single number that depends on the elements of the matrix A. Determinants exist only for square matrices (i.e., ones where the number of rows equals the number of columns).  

Determinants are a basic building block of [[linear algebra]], and are useful for finding areas and volumes of geometric figures, in [[Cramer's rule]], and in many other areas ways. The determinant is equal to the product of the [[eigenvalue]]s of a matrix.

Determinants are a basic building block of [[linear algebra]], and are useful for finding areas and volumes of geometric figures, in [[Cramer's rule]], and in many other areas ways. If the [[characteristic polynomial]] splits into linear factors, then he determinant is equal to the product of the [[eigenvalue]]s of a matrix, counted by their algebraic multiplicities.

== Motivation ==

== Motivation ==