What is matrix and its types – Matrix is a arrangement of elements
The origin of Matrix is that it is derived from Latin word “mater” which means mother and “matrix” means breeding female basically.
In mathematics, we use this term to display data in a square brackets”[ ]” in the form of rows and columns.Following is the answer of What is matrix and its types in mathematics.
Matrix is the rectangular array of real numbers (R) in rows and columns.
All the numbers in matrices are called elements or entities of matrix.
Here, A shows entries and numbers show order of entry.
Types of matrix:
Different types of matrix and their examples are following:
If a matrix has only one row then it is called as row matrix.
Row matrix is
This matrix has one row and four column.
If a matrix has only one column then it is called as column matrix.
is column matrix.
A matrix is rectangular only if number of rows are not equal to number of column.
Rectangular Matrix of order 3by4 is following:
Unlike rectangular matrix, a square matrix has number of rows equal to number of column.
This is the square matrix of 3by3.
Negative of a Matrix:
Negative of a matrix is obtained by changing the signs of all the entries of the matrix.
Multiplying by “–” to a matrix, negative matrix is formed.
If all elements of a matrix are zero whether there are one element or many in the matrix, it is zero or null matrix.
Zero matrix of 3by3 is
Transpose of Matrix:
When all the columns are changed into rows or all the rows are changed into columns, then the obtained matrix is called transpose of a matrix.
By changing the rows of a matrix into column, the resultant matrix become transpose of that matrix.
When transpose of matrix equals to original matrix then it is Symmetric matrix.
As in given example, “A=At ” so it is symmetric matrix.
When transpose of matrix equals to negative of original matrix then it is called Skew-symmetric matrix.
In this example “At” equals to “-A“. Thus, this matrix is skew-symmetric.
A matrix is called diagonal matrix if atleast one element of diagonal is not zero and all non-diagonal matrix are equal to zero.
General example of diagonal matrix is below
A matrix is called scalar matrix if all the element of diagonal are same but not zero and all non-diagonal matrix are equal to zero.
Example of scalar matrix is
If all the element of diagonal are one and all non-diagonal matrix are equal to zero, then it is called identity matrix.
The identity matrix of order 3by3 is