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
