Introduction to Determinants

The term determinant was first introduced by Gauss in 1801 while discussing quadratic forms. He used the term because the determinant determines the properties of the quadratic forms.

To every square matrix A of order n with entries as real or complex numbers, you can associate a number called determinant of matrix A and it is denoted by |A| or det(A) or ∆.

Difference between a matrix and a determinant

  1. A matrix cannot be reduced to a number. That means a matrix is a structure alone and is not having any value. But a determinant can be reduced to a number.
  2. The number of rows may not be equal to the number of columns in a matrix. In a determinant the number of rows is always equal to the number of columns.
  3. On interchanging the rows and columns, a different matrix is formed. In a determinant interchanging the rows and columns does not alter the value of the determinant.