__Null Matrix __:-

MAtrix with all elements O.

__Transpose of a Matrix__:- The matrix obtaired from a given matrix A, by inter changing rows and columns is called transpose of A and is denoted by a

^{T} . or A

^{1}.

__Properties of Transpose (Secondary In formation)__:-

(i) (A

^{T})

^{T} = A

(ii) (A + B)

^{T} = A

^{T} + B

^{T}
(iii) (

A)

^{T} =

. A

^{T}
(iv) (A B)

^{T} = B

^{T} A

^{T}.

__Conjugate of a Matrix__:- A matrix obtained from any given matrix A coutaining complex number as its elements, or replaing its elements by the corresponding conjugate complex no is called conjugate of A and is denoted by

.

__Properties of conjugate (Secondary Information__:-

(i)

= A

(ii)

(iii)

(iv)

__Transpose Conjugate of a Matrix__:-

The transpose of conjugate of a matrix denoted by

.

__Properties of Transpose of conjugate__:-

(Secondary Information):-

(i)

(ii)

(iii)

(iv)

__ALGEBRA OF MATRICES__:-

__Addition and Subtraction__:- Any two matrices can be added lif they are of same order and the (or Subtrected)

resulting matrix is of same order, corresponding elements are added or subtracted .

__Scalar Multiplication__:-

The matrix obtained by multiplleying every element of by a scalar

is called the scalar multiple of A by

and is denoted by

A .

__Multipliecation of Matrices__:-

Two matrices can be multiplied lonly when the no of columns in the first is equal to the no . of rows inm the second. Such matrices are called conformable for multiplication.

If A B = c

A - [a

_{ij}]

_{ mXn} B - [b

_{ke}]

_{ nXp}
C

_{ij}^{2} a

_{ ik} b

_{ kj}
__Special Matrices (Secondary Information__:-

__Symmetric and Skew Symmetric Matrices__:-

A square matriex is A is said to be symmetric if

A = A

^{T}.

and skew symmetric if A = - A

^{T}.

__Unitary Matrix__
A matrix is unitary if

A = 1