The document presents information on matrices and their types. It defines a matrix as an arrangement of numbers, symbols or expressions in rows and columns. It discusses different types of matrices including row matrices, column matrices, square matrices, rectangular matrices, diagonal matrices, scalar matrices, unit/identity matrices, symmetric matrices, complex matrices, hermitian matrices, skew-hermitian matrices, orthogonal matrices, unitary matrices, and nilpotent matrices. It provides examples and definitions for hermitian matrices, orthogonal matrices, idempotent matrices, and nilpotent matrices. The presentation was given by Himanshu Negi on matrices and their types.

1. MATHEMATICS
PRESENTATION ON
MATRICES AND ITS TYPE
NAME : HIMANSHU NEGI
SECTION : F
BRANCH : CSE

2. WHAT IS MATRIX OR MATRICES
GENERALLY MATRICES IS A PLURAL OF MATRIX
DEFINITION:
A matrix is an arrangement of numbers,
symbols, or expressions in rows and columns.
ORDER OF A MATRIX:
(Number of rows X number of columns)
is considered as an order of matrix

3. TYPES OF MATRIX
 ROW MATRIX : having only row elements.
 COLUMN MATRIX: having only column elements.
 SQUARE MATRIX : whose order is (nXn).
 RECTANGULAR MATRIX : whose column elements are not equal to row
element.
 DIAGNAL MATRIX : A square matrix is called a diagonal matrix if all its
diagonal elements are non zero.
 SCALAR MATRIX: a diagonal matrix in which all diagonal elements are
equal to a scalar quantity.
 UNIT OR IDENTITY MATRIX: a square matrix in which all the diagonal
elements are equal to unity and non diagonal elements are non zero.
 SYMMETRIC MATRIX: a matrix in which ij element =ji element or A=A’.
SOME BASIC TYPES OF MATRICES

4. SOME OTHER TYPES OF
MATRICES
 COMPLEX MATRIX
 HERMITION MATRIX
 SKEW HERMITION MATRIX
 ORTHOGONAL MATRIX
 UNITARY MATRIX
 NILPOTENT MATRIX

5. HERMITIAN MATRIX
 A hermitian matrix must be a square matrix
of order (nXn).
 For a matrix to be a hermitian matrix, the i-j
element of matrix A should be equal to the
conjugate of j-i element.
 A necessary condition of hermitian matrix is
A=(A)`
Eg. 1 2+3i 3+i
2-3i 2 1-2i
3-i 1+2i 5

6. •Orthogonal matrix:
when the product of matrix A and transpose
of it is equal to identity matrix.
A.A’ = I
• Idempotent matrix:
when the square of a matrix is equal to that matrix.
A
2
= A
•Nilpotent matrix:
when A = 0 or null matrix.
k
Where k is a positive integer.

7. THANK YOU