Basic Mathematics: Matrix Part 1

Square Matrix:

 ü Same number of rows and columns

 ü Order of the matrix is the no of rows or columns

 ü  The diagonal of the matrix is called as principal diagonal

 ü The sum of the diagonal elements is Trace of the Matrix

Rectangular Matrix:

 ü  Number of rows ≠ Number of columns

Diagonal Matrix:

 ü  A square Matrix in which all the elements except diagonal elements are zero

Unit Matrix (Identity Matrix):

 ü All diagonal elements are ‘1’

 ü Denoted by symbol ‘I’

Null Matrix:

 ü All elements in the matrix is zero

Symmetric Matrix:

 ü  Aᵀ=A

Skew-Symmetric Matrix:

 ü Aᵀ=-A

 ü Note : All diagonal elements of skew-symmetric matrix is zero

Triangular Matrix:

 ü Upper Triangular Matrix: All the elements below its principal diagonal are zero

 ü  Lower Triangular Matrix: All the elements above its principal diagonal are zero

Orthogonal Matrix:

 ü Aᵀ.A=I

Singular Matrix:

 ü  |A|=0

Unitary Matrix:

 ü Aᶿ= (Ᾱ)ᵀ

Hermitian Matrix:

 ü Aᶿ=A

 ü Diagonal elements are always real

Skew-Hermitian Matrix:

 ü Aᶿ=-A

 ü Diagonal elements are either zero or pure imaginary

Idempotent Matrix:

 ü A²=A

Scalar Matrix:

 ü All diagonal elements are equal

Nilpotent Matrix;

 ü Aⁿ=0, n is called index of nilpotent matrix A