Matrices

Matrices

1. Order or Size of matrix (mxn)

   • Row matrix (1xn)
   • Column matrix (mx1)
   • Square matrix (mxm)
     • Principal Diagonal
       • Diagonal matrix
       • Scalar matrix
       • Constant matrix
       • Identity matrix
       • Upper triangular matrix
       • Lower triangular matrix
       • Trace of a matrix
     • Determinant det(A)
       • Singular matrix det(A)=0
       • Non singular matrix
         • Cofactor matrix
         • Adjoint matrix
         • Inverse matrix
   • Rectangular matrix (mxn) m and n are not samw
   • Zero matrix

2. Addition A+B

3. Subtraction A-B

4. Multiplication A.B

   • Idempotent matrix
   • Involutory
   • Nilpotent matrix
     • Index of the matrix
   • Periodic Matrix
     • Period of the matrix

5. Transpose A'

   • Symmetric A'=A
   • Skew Symmetric A'= - A
   • Orthogonal matrix A.A'=I

6. Linear System of equations

   • Matrix inversion method
   • Crammer's method

7. Conjugate matrix

   • Conjugate transpose
     • Hermitian matrix
     • Skew hermitian matrix
     • Unitary matrix