INTRODUCTION:
Matrices were
formulated and developed as the concept during 18th and 19th
centuries. Matrices are useful because they enable us to consider an array of
many numbers as a single object and perform calculations with these symbols in
a very compact form.
DEFINITION
OF MATRICES
A matrix is a rectangular array of numbers in row and columns
enclosed within a square brackets
TYPES OF
MATRICES
ROW MATRIX
A matrix
said to be a row matrix if it has only one row. A row matrix is also called as
a row vector.
EXAMPLEA=(5 4 6 7)
COLUMN
MATRIX
A matrix is
said to be a column matrix if it has only one column. It is also called as a
column vector
EXAMPLE
A=
and
and
B=
are the column matrix of order 2*4 and 3*1 respectively
are the column matrix of order 2*4 and 3*1 respectively
SQUARE
MATRIX
A matrix in
which the number of rows and the number of columns are equal is said to be a
square matrix .
EXAMPLE
A=
B= 
are square
matrices of orders 2 and 3 respectively
are square
matrices of orders 2 and 3 respectively
DIAGNOAL
MATRIX
A diagonal
matrix in which all the leading diagonal entries are 1 is called the unit matrix.
EXAMPLE
A=
B= 
are
diagonal matrices of orders 2 and 3 respectively.
are
diagonal matrices of orders 2 and 3 respectively.
SCALAR
MATRIX
A diagonal
matrix in which all the elements along the leading diagonal are equal to a
non-zero constant is called a scalar matrix.
EXAMPLE
A=
B= 
are the scalar
matrix of order 2 and 3 respectively.
are the scalar
matrix of order 2 and 3 respectively.
UNIT
MATRIX
A diagonal
matrix in which all the leading diagonal entries are 1 is called the unit
matrix.
EXAMPLE
I = 
are unit matrices of
orders 2 and 3 respectively.
are unit matrices of
orders 2 and 3 respectively.
NULL OR
ZERO MATRIX
A matrix is
said to be a null matrix or zero-matrix if each of its elements is zero. It is
denoted by o.
EXAMPLE
O= 
are the
null matrices of order 2*2
are the
null matrices of order 2*2
TRANPOSE
OF A MATRIX
The
transpose of a matrix A is obtained by interchanging rows and column
of the matrix A and it is denoted by A transpose.
EXAMPLE
A= 
Transpose of A=
APPLICATION
OF MATRIX
Computer
have embedded matrix arithmetic in graphic processing algorithms especially to
render reflection and refraction.
The field of
probabilities and statistics may use matrix representations.
Before
computer graphics, the science of optics used matrix mathematics to account for
reflection and for refraction.
Mathematics,
scientists and engineers represent groups of equation as matrices.
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