Thursday, 25 February 2016
Level: BA/Bsc
Subject: mathematical economics
Types of Matrices:
Column matrix:
A matrix is said to be a column matrix if it has only one column. For example, below is a column matrix of order 3×1
Row matrix:
A matrix is said to be a row matrix of it has only one row. For example , below is a row matrix of order 3×1
Square matrix:
A matrix is said to be a square matrix if its number of rows are equal to the number if its columns. Thus m×n matrix is said to be a square matrix if m=n and is known as a square matrix of order 'n' . For example:
Matrix A is a square matrix of order 2
While, matrix B is a square matrix of order 3.
Equal matrix:
Two matrix are equal if their corresponding elements are equal. If two matrices fulfill the following conditions, they are said to be equal:
- Each matrix has the same number of rows.
- Each matrix aphas the same number of columns.
- Corresponding elements within each matrix are equal.
Consider the three matrices shown below.
If A=B , we know that x=3 and y=0; since corresponding elements of equal matrices are also equal. And we know that the matrix C is not equal to A or B because C has more columns than A or B.
Diagonal matrix:
A square matrix is said to be a diagonal matrix if all its non diagonal elements are zero. For example,
Scalar Matrix:
A diagonal matrix is said to be a scalar matrix if its diagonal elemennts are equal. For example,
are scalar matrices of order 2 and 3, respectively.
Identity matrix:
A square matrix in which elements in the diagonal are all 1 and rest of the elements are all zero is called an identity or unit matrix.
For example,
Note:
A scalar matrix is an identity matrix when k=1. But every identity matrix is clearly a scalar matrix. The identity matrix has a unique feature that ifbanmatrix that is multiplied by identity matrix remains the same; that is: AI=IA=A
Null matrix:
A matrix is said to be zero matrix or null matrix if all its elements are zero.
For example,
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