Matrices
Definition of Matrices:
A rectangular array of entries is called a Matrix. The entries may be real, complex or functions.
The entries are also called as the elements of the matrix.
The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital letters.
Matrices are one of the most powerful tools in mathematics.The
evolution of concept of matrices is the result of an attempt to obtain compact and
simple methods of solving system of linear equations. Matrices are not only used as a
representation of the coefficients in system of linear equations, but utility of matrices
far exceeds that use.
Now let us learn about the different types of Matrices.It is easy to understand Matrices if we learn its types.We might come across some very common questions in various math text book that ask about the types of matrices.
In this section, we shall discuss different types of matrices.
1) Column matrix:
A matrix is said to be a column matrix if it has only one column.
2)Row matrix
A matrix is said to be a row matrix if it has only one row.
3)Square matrix
A matrix in which the number of rows are equal to the number of columns, is
said to be a square matrix. Thus an m × n matrix is said to be a square matrix if
m = n and is known as a square matrix of order ‘n’.
4)Diagonal matrix
A square matrix B = [bij] m × m is said to be a diagonal matrix if all its non
diagonal elements are zero, that is a matrix B = [bij] m × m is said to be a diagonal
matrix if bij = 0, when i ≠ j.
5)Scalar matrix
A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal,
that is, a square matrix B = [bij] n × n is said to be a scalar matrix if
bij = 0, when i ≠ j
bij = k, when i = j, for some constant k.
6)Identity matrix
A square matrix in which elements in the diagonal are all 1 and rest are all zero
is called an identity matrix.
7)Zero matrix
A matrix is said to be zero matrix or null matrix if all its elements are zero.
Hope you like the above example of Matrices.
Please leave your comments, if you have any doubts.
Definition of Matrices:
A rectangular array of entries is called a Matrix. The entries may be real, complex or functions.
The entries are also called as the elements of the matrix.
The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital letters.
Example:
(i)Matrices are one of the most powerful tools in mathematics.The
evolution of concept of matrices is the result of an attempt to obtain compact and
simple methods of solving system of linear equations. Matrices are not only used as a
representation of the coefficients in system of linear equations, but utility of matrices
far exceeds that use.
Now let us learn about the different types of Matrices.It is easy to understand Matrices if we learn its types.We might come across some very common questions in various math text book that ask about the types of matrices.
In this section, we shall discuss different types of matrices.
1) Column matrix:
A matrix is said to be a column matrix if it has only one column.
2)Row matrix
A matrix is said to be a row matrix if it has only one row.
3)Square matrix
A matrix in which the number of rows are equal to the number of columns, is
said to be a square matrix. Thus an m × n matrix is said to be a square matrix if
m = n and is known as a square matrix of order ‘n’.
4)Diagonal matrix
A square matrix B = [bij] m × m is said to be a diagonal matrix if all its non
diagonal elements are zero, that is a matrix B = [bij] m × m is said to be a diagonal
matrix if bij = 0, when i ≠ j.
5)Scalar matrix
A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal,
that is, a square matrix B = [bij] n × n is said to be a scalar matrix if
bij = 0, when i ≠ j
bij = k, when i = j, for some constant k.
6)Identity matrix
A square matrix in which elements in the diagonal are all 1 and rest are all zero
is called an identity matrix.
7)Zero matrix
A matrix is said to be zero matrix or null matrix if all its elements are zero.
Hope you like the above example of Matrices.
Please leave your comments, if you have any doubts.
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