Difference between revisions of "Scilab/C2/Matrix-Operations/English-timed"

| | Welcome to the spoken tutorial on Matrix Operations.

| | Access the elements of Matrix

| |Determine the determinant, inverse and eigen values of a matrix.

| |Define special matrices.

| | Perform elementary row operations.

| | Solve the system of “linear equations”.

| | The prerequisites are

| |''You should have listened to the Spoken Tutorial: Getting started with Scilab and '''Vector Operations.

| |I am using Windows 7 operating system and Scilab 5.2.2 for demonstration.

| | Recall that in the Spoken Tutorial, 'Vector Operations',

| | matrix E was defined as E is equal to open square bracket 5 space 19 space 15 semicolon 8 space 22 space 36 close the square bracket and press enter

| |For example, first row of E can be obtained using the following command: E1 = E into bracket 1 comma colon and press enter

| |The command returns all the elements of the first row in the order of their appearance in the row.

| |Colon, when used alone, refers to all the elements of row or column, depending upon whether it appears as a first or a second entry respectively inside the bracket.

| E2 = E of colon comma 2 colon 3 close the bracket and press enter

| | If the size of the matrix is not known $ (dollar ) symbol can be used to extarct the last row or column of that matrix.

| Elast col= E into brackets colon comma dollar sign close the bracket and press enter

| |Now, let us learn how to calculate the determinant of a square matrix using the command “det”

| |Recall that in the Spoken Tutorial, Vector Operations, we had defined A as

| |A = open square bracket 1 space 2 space minus 1 semicolon  -2 space  - 6 space 4 semicolon -1 space  -3 space 3 close the square bracket and press enter

| |Let us calculate the determinant of A by the command det of A  and press Enter.

|| To calculate the inverse and the eigenvalues of a matrix, the commands, “inv” and “spec” respectively, can be used.

|| For example: inv of A  gives the inverse of A and spec of A gives the eigen values of  matrix A

| |See 'help spec' to see how eigenvectors can also be obtained using this command.

| |Square or cube of a square matrix A can be calculated by simply typing A square  or A cube '''respectively'''.

| |Please pause the tutorial now and attempt the exercise number one given with the video.

| | Certain special matrices can also be created in Scilab:

| |For example a matrix of zeros with 3 rows and 4 columns can be created using “zeros” command

| |zeros into bracket 3 comma 4  and press enter

| |A matrix of all ones can be created with “ones” command as follows

| |ones into bracket 2 comma 4  gives a matrix of all ones

| |It is easy to create an identity matrix using the  “eye” command:

| ' e y e' of 4 comma 4 gives a 4 by 4 identity matrix

| |A user may need a matrix consisting of pseudo random numbers. It can be generated using the “rand” command as follows:

| |p=rand into bracket 2, 3  and press enter

| |Recall that in the Spoken Tutorial,Vector Operations, we had defined the matrix P as follows.

| |P = open square bracket 1 space 2 space 3  semicolon 4 space 11 space 6  close the square bracket and press enter

| |P into bracket 2 comma colon is equal to  P into bracket 2 comma colon  minus 4 multiplied by P into bracket 1 comma colon and press enter

| |T =  open square bracket P semicolon, open another square bracket write down  the elements 5 5 -2 close both the square bracket and press enter

| |The semicolon after P states that anything after it should go to the next row. '

| |The above set of equations can be written in the Ax = b form.

| | The solution is then given as inverse of A times b

| |A is defined as A =  open square bracket 1 space  2 space  -1 semicolon -2 space -6 space 4 semicolon -1 space  -3 space  3 close the square bracket and press enter

| |B can be defined as b  is equal toSquare bracket 1 semicoln -2 semicolon 1 close the square bracket and press enter

| |The solution, x, can be obtained using x = inv  of A multiplied by b

| |It is worth noting that it is a small letter 'i' in the command, 'inv'.

| |Alternatively, the same result can be achieved using a backslash operation in Scilab.

| |Lets do this in Scilab x  is equal to A backslash b and press enter.

| |It gives the same result. Type "help backslash" and "help inv" in Scilab to know more about individual advantages and disadvantages.

|A multiplied by x minus b

| |However, one will indeed get a very small number, typically of the order of 10 raised to -16

| Please pause the tutorial now and attempt exercise number two given with the video.

| This brings us to the end of this spoken tutorial on Matrix Operation.

| |In this tutorial we have learnt

| | To access the element of the matrix using the colon operator

| | Calculate the inverse of a matrix using the 'inv' command or by backslash

| |Calculate the derterminant of matrix using 'det' command.

| |Calculate eigen values of a matrix using 'spec' command.

| |Define a matrix having all the elements one, Null Matrix,  Identity matrix and a matrix with random elements by using functions ones(), zeros(), eye(), rand() respectively

| |This spoken tutorial has been created by the Free and Open Source Software in Science and Engineering Education(FOSSEE).

| |This is Anuradha Amrutkar from IIT Bombay signing off.