MATRICES
01. MATRIX 02. ORDER
A matrix is an ordered rectangular array of numbers or A matrix having m rows and n column
simply m×n matrix.
functions. The numbers or functions are called the
elements of the matrix or A=[aij ]m×n , 1≤ i ≤ m, 1 ≤ j ≤ n, i, j N
aij is an element lying in the ith row & jt
in m×n matrix will be mn.
03. TYPE OF MATRIX
(i) Column Matrix: A matrix is said to be a column matrix if it has only one column, i.e., A=[aij]m×1 is a co
(ii) Row Matrix: Row matrix has only one row, i.e., B=[bij]1×n is a row matrix of order 1×n.
(iii) Square Matrix: Square matrix has equal number of rows and columns, i.e., A=[aij]m×m is a square m
(iv) Diagonal Matrix: A square matrix is said to be diagonal matrix if all of its non-diagonal elements a
diagonal matrix if bij=0, where i ≠ j.
(v) Scalar Matrix: It is a diagonal matrix with all its diagonal elements are equal, i.e., B=[bij ]m×n is a scal
I = j & k= constant.
(vi) Identity Matrix: : It is a diagonal matrix having all its diagonal elements equal to 1, i.e., A=[aij ]m×n is
a ij = {
1, if i = j
0, if i ≠ j
we denote identity matrix by In when order is n.
(vii) Zero Matrix: A matrix is said to be zero or null matrix if all its elements are zero. It is denoted by O.
04. EQUALITY OF MATRICES 05. TRA
The sum of diag
Two matrices A=[aij] and B = [bij] are said to be equal if called the trace
(i) they are of the same order n
(ii) each element of A is equal to the corresponding element of B, i.e., aij = bij for all i & j tr A= ∑a
i =1
ii
= a11
Properties of Tr
Let A = [aij]n × n a
06. ADDITION OF MATRICES (i) tr (λA) = λtr(
(iii) tr(AB) = tr(B
01. MATRIX 02. ORDER
A matrix is an ordered rectangular array of numbers or A matrix having m rows and n column
simply m×n matrix.
functions. The numbers or functions are called the
elements of the matrix or A=[aij ]m×n , 1≤ i ≤ m, 1 ≤ j ≤ n, i, j N
aij is an element lying in the ith row & jt
in m×n matrix will be mn.
03. TYPE OF MATRIX
(i) Column Matrix: A matrix is said to be a column matrix if it has only one column, i.e., A=[aij]m×1 is a co
(ii) Row Matrix: Row matrix has only one row, i.e., B=[bij]1×n is a row matrix of order 1×n.
(iii) Square Matrix: Square matrix has equal number of rows and columns, i.e., A=[aij]m×m is a square m
(iv) Diagonal Matrix: A square matrix is said to be diagonal matrix if all of its non-diagonal elements a
diagonal matrix if bij=0, where i ≠ j.
(v) Scalar Matrix: It is a diagonal matrix with all its diagonal elements are equal, i.e., B=[bij ]m×n is a scal
I = j & k= constant.
(vi) Identity Matrix: : It is a diagonal matrix having all its diagonal elements equal to 1, i.e., A=[aij ]m×n is
a ij = {
1, if i = j
0, if i ≠ j
we denote identity matrix by In when order is n.
(vii) Zero Matrix: A matrix is said to be zero or null matrix if all its elements are zero. It is denoted by O.
04. EQUALITY OF MATRICES 05. TRA
The sum of diag
Two matrices A=[aij] and B = [bij] are said to be equal if called the trace
(i) they are of the same order n
(ii) each element of A is equal to the corresponding element of B, i.e., aij = bij for all i & j tr A= ∑a
i =1
ii
= a11
Properties of Tr
Let A = [aij]n × n a
06. ADDITION OF MATRICES (i) tr (λA) = λtr(
(iii) tr(AB) = tr(B
