Determinant
Determinant
The determinant of a matrix is a special number that can be calculated from a square matrix . The determinant of a matrix A is denoted det ( A ), det A , or | A |.
The determinant tells us things about the matrix that is useful in systems of linear equations , helps us find the inverse of a matrix , and is useful in calculus , Computer Science , Chemistry , Geoemetry and more .
Properties of Determinants
o The determinant is a real number , it is not a matrix . o The determinant can be a negative number .
o
It is not associated with absolute value at all except that they both use vertical lines .
o The determinant only exists for square matrices ( 2 × 2 , 3 × 3 , ... n × n ). The determinant of a 1 × 1 matrix is that single value in the determinant .
o The inverse of a matrix will exist only if the determinant is not zero . o For matrix A , | A | is read as determinant of A and not modulus of A .
o
Only square matrices have determinants
Determinant of a matrix of order one Let A = [ a ] be the matrix of order 1 , then determinant of A is defined to be equal to a
Determinant of a matrix of order two