MATRICES AND ITS TYPE

a short explanation on different types of matrices

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.

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