Matrix

A matrix is a rectangular array of numbers arranged into rows and columns.

Types of Matrices

1. Row matrix

         A matrix having one row and any number of columns is a row matrix

  E.g.: A = [a b c d]1xn

2. Column matrix

         A matrix having one column and any number of rows is known as column matrix.

 3.Zero matrix

         A zero or null matrix is one whose elements are zeroes.

 4. Square matrix

         A matrix having same number of rows and columns is known as a square matrix.

 5. Diagonal matrix

        A square matrix having non-zero entries only on the main diagonal is known as diagonal matrix.

 6. Scalar matrix

        A diagonal matrix with equal non-zero entries on the same diagonal is known as scalar matrix.

 7. Unit matrix (Identity matrix)

         A diagonal matrix is a unit matrix each of the diagonal elements is unity.

Transpose of a matrix

          The transpose of a matrix A is the matrix obtained by interchanging the rows and columns of A, and is denoted by A1 or AT.

              (A1)1 = A

              (A+B)1 = A1 + B1

                     (AB)1 = B1A1

              (kA)1 = kA1, where k is a complex number

 

Symmetric matrices

          A square matrix is said to be symmetric if A1 = A.

Skew-Symmetric matrices

          A square matrix A is said to be skew-symmetric if A1 = -A.

Determinants

         To each square matrix A = [aij] we associate a number called determinant of A and is denoted by |A|.  Matrices which are not square do not have determinants.

Singular and non-Singular matrices

         A square matrix A is called singular if |A| = 0.  If |A| ¹ 0 then A is called non-singular.

Leave a Reply

Your email address will not be published. Required fields are marked *