 working as an assistant professor in Wolchen Institute of Technology, Sulapur. Today we are going to see matrix operations using SILAB, Learning Outcome. At the end of the session, students will be able to perform basic arithmetic and matrix operations using SILAB. So, these are the outline, basic arithmetic operations on matrices, basic matrix processing. So, let's see basic arithmetic operations. First operation, addition. Second, subtraction. Third, multiplication. Fourth, division. Let's see the first operation that is addition. Let's define 2 by 2 matrix, matrix A having 4 elements that is 2 rows and matrix B, 2 by 2 matrix A and 2 by 2 matrix B. For addition operation, the plus operator is used for the operation. Here we get the result as 3, 5, 7, 9 which is the addition of matrix A and matrix B. 1 plus 2 is 3, 2 plus 3 is 5, 3 plus 4 is 7 and 4 plus 5 is 9. Next operation, subtraction. For subtraction operation, we use minus sign. So, let's define matrix 2 by 2 matrix A and 2 by 2 matrix B. Here, we get the result as 1, 1, 1, 1 as the matrix A and matrix B are subtracted that is 2 minus 1, 4 minus 3, 5 minus 4 and 3 minus 2. So, the answer is a square matrix that is 1, 1, 1 and 1. Next operation that is multiplication. For this operation, a star operator is used. Let's define square matrix that is 2 by 2 matrix having elements 1, 2, 3 and 4 and second matrix having 2 rows, 2, 3 and second row 4, 5. Here the matrix multiplication results in 10, 13, 22 and 29 as the multiplication of A and matrix B is occurred. So, the main dimension of matrix is the basic matrix finding the dimension of matrix is very important. To find out the dimension of matrix, the operator size is used. Let's define a 3 by 3 matrix having elements 1st row 11, 12, 13, 2nd row 21, 22, 23, 3rd row 31, 32 and 33. So, for finding the dimension of a matrix a function size S, I, Z, D is used so that it determines 3 and 3 that is it has 3 rows and 3 columns. In the same way the diagonal elements of a matrix can be found out by using a diagonal operator that is D, I, A, G which is used to find out the diagonal elements of a matrix. Here the diagonal elements of a matrix are 11, 22 and 33. So, when a function D, I, A, G is given it shows the diagonal elements of a matrix. Next trace of a matrix can be found out trace of a matrix is nothing but addition of the diagonal elements when the diagonal elements are found out the addition of the diagonal elements is nothing but the trace of a matrix that is the answer is 66 here it is 11 plus 22 plus 33 that is 66 trace of matrix A is 66 when a vector is defined when a vector is defined with a random number of variables the minimum the element which is minimum can be found out by using function m, i, n that is when a vector x is defined as 5, 10, 15 and 20 so when a operator m, i, n is used then it gives us 5 because 5 is the minimum element defined in the vector. In the same way the maximum element in the vector can be found out by using a function m, a, x as we see here vector x is defined as 5, 10, 15 and 12 so when a vector m, a, x is used then it gives 15 that is 15 is the maximum element in the defined in a vector we can also find the mean of a vector mean is nothing but the average of all the elements that is when a vector x is defined as 5, 10, 15 and 12 the addition that is 5 plus 10 plus 15 plus 12 divide by 5 that gives 10.5 so in this way mean of a vector can also be found out so I just want you to pause the video for few seconds and list down few matrix operations you know let's see so this is the upper triangular matrix lower triangular matrix and transpose so what is lower triangular matrix a matrix which contains the diagonal elements and elements below the diagonal so let's see how to find out lower triangular matrix so a matrix A is defined as 3 by 3 matrix consisting of 11, 12, 13, 21, 22, 23, 31, 32 and 33 so when a function t, r, i, l is used diagonal elements and the elements which are below the diagonal in the same way we can found out upper triangular matrix upper triangular matrix is a matrix which has a diagonal elements and the elements above the diagonal when a matrix 3 by 3 is defined as 11, 12, 13 21, 22, 23, 31, 32 and 33 so when we use a function t, r, i, u of a matrix A then you see the output comes as upper triangular matrix that is diagonal elements and the elements above the diagonal so let's see a transpose transpose of a matrix is nothing but a row is converted into column and the column is converted into row either row or columns are converted vice versa so in this dash operator is used a 3 by 3 matrix is defined 11, 12, 13, 21, 22, 23, 31, 32, 33 so when a dash operator is used a dash operator is used it converts first row that is 11, 12, 13 as a first column 21, 22, 23 as a second column and 31, 32, 33 as a third column so transpose of a matrix can also be found out on the psi lab eigenvalues and eigenvectors can also be found out in psi lab by using psi lab so let's define a matrix 2 by 2 matrix that is 1, 2, 3, 4 the function spec is used for finding the eigenvalues that is we have found out that is as you see here the output for eigenvalues given here and the eigenvalues and eigenvalues after finding the eigenvalues eigenvectors are also found out as you see here so references are book, modeling and simulation in psi lab psi course by Stephen Campbell a book, psi lab by Hema Ramchandran and S. Nair thank you