Matrices in robotics and automation
In robotics and automation, matrices are the base elements for the robot movements. The movements of the robots are programmed with the calculation of rows and columns of matrices. The inputs for controlling robots are given based on the calculations from matrices.
|Elements of a rectangular matrix
|Q: The order of a matrix A is 3 × 5. List its elements in each row in general form.
| Sol: The matrix has 3 rows and 5 columns i.e, m = 3 and n = 5
The total number of elements = m.n = 15
The general form of an element = aij
The max. value of i = m = 3
The max. value of j = n = 5
∴ i takes the values 1, 2 & 3
and j takes the values 1, 2, 3, 4 & 5
For i = 1, the elements in first row are:
a11, a12, a13, a14, a15
For i = 2, the elements in second row are:
a21, a22, a23, a24, a25
For i = 3, the elements in third row are:
a31, a32, a33, a34, a35
A matrix is usually represented by an upper–case letter such as A, B, P, Y etc.
Its elements are represented by corresponding lower–case letters with two subscript indices such as eg: a11, b21, p43, y23 etc.
In general, aij represents an element of the matrix A occurring in ith row and jth column.
In the 2 × 2 matrix
a11 represents the element in the first row and first column;
a12 represents the element in the first row and second column;
a21 represents the element in the second row and first column and
a22 represents the element in the second row and second column.
General form of a matrix:
In general, a set of 'mn' elements can be arranged as a matrix having 'm' rows and 'n' columns as below:
Or in short,
A = [aij]m × n
In the above matrix, aij represents an element of the matrix A occurring in ith row and jth column.
The maximum value of 'i' can be 'm' i.e, the number of rows and
the maximum value of 'j' can be 'n' i.e, the number of columns.
In general, any matrix of the order m × n is called a rectangular matrix.