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Diffstat (limited to 'matrices/script.rst')
| -rw-r--r-- | matrices/script.rst | 40 |
1 files changed, 25 insertions, 15 deletions
diff --git a/matrices/script.rst b/matrices/script.rst index fa30811..9b305d5 100644 --- a/matrices/script.rst +++ b/matrices/script.rst @@ -22,8 +22,10 @@ Welcome to the spoken tutorial on Matrices. {{{ switch to next slide, outline slide }}} -In this tutorial we will learn about matrices, creating matrices and -matrix operations. +In this tutorial we will learn about matrices, creating matrices using +direct data, by converting a list, matrix operations. Finding inverse +of a matrix, determinant of a matrix, eigen values and eigen vectors +of a matrix, norm and singular value decomposition of matrices. {{{ creating a matrix }}} @@ -70,6 +72,8 @@ Similarly, it does matrix subtraction, that is element by element subtraction. Now let us try, + +{{{ Switch to next slide, Matrix multiplication }}} :: m3 * m2 @@ -86,6 +90,8 @@ function ``multiply()`` multiply(m3,m2) +{{{ switch to next slide, Matrix multiplication (cont'd) }}} + Now let us see an example for matrix multiplication. For doing matrix multiplication we need to have two matrices of the order n by m and m by r and the resulting matrix will be of the order n by r. Thus let us @@ -106,11 +112,15 @@ in matrix object. {{{ switch to next slide, recall from arrays }}} -As we already saw in arrays, the functions ``identity()``, -``zeros()``, ``zeros_like()``, ``ones()``, ``ones_like()`` may also be -used with matrices. +As we already saw in arrays, the functions ``identity()`` which +creates an identity matrix of the order n by n, ``zeros()`` which +creates a matrix of the order m by n with all zeros, ``zeros_like()`` +which creates a matrix with zeros with the shape of the matrix passed, +``ones()`` which creates a matrix of order m by n with all ones, +``ones_like()`` which creates a matrix with ones with the shape of the +matrix passed. These functions can also be used with matrices. -{{{ switch to next slide, matrix operations }}} +{{{ switch to next slide, more matrix operations }}} To find out the transpose of a matrix we can do, :: @@ -120,9 +130,9 @@ To find out the transpose of a matrix we can do, Matrix name dot capital T will give the transpose of a matrix -{{{ switch to next slide, Euclidean norm of inverse of matrix }}} +{{{ switch to next slide, Frobenius norm of inverse of matrix }}} -Now let us try to find out the Euclidean norm of inverse of a 4 by 4 +Now let us try to find out the Frobenius norm of inverse of a 4 by 4 matrix, the matrix being, :: @@ -131,17 +141,17 @@ matrix, the matrix being, The inverse of a matrix A, A raise to minus one is also called the reciprocal matrix such that A multiplied by A inverse will give 1. The -Euclidean norm or the Frobenius norm of a matrix is defined as square -root of sum of squares of elements in the matrix. Pause here and try -to solve the problem yourself, the inverse of a matrix can be found -using the function ``inv(A)``. +Frobenius norm of a matrix is defined as square root of sum of squares +of elements in the matrix. Pause here and try to solve the problem +yourself, the inverse of a matrix can be found using the function +``inv(A)``. And here is the solution, first let us find the inverse of matrix m5. :: im5 = inv(m5) -And the euclidean norm of the matrix ``im5`` can be found out as, +And the Frobenius norm of the matrix ``im5`` can be found out as, :: sum = 0 @@ -166,11 +176,11 @@ The solution for the problem is, {{{ switch to slide the ``norm()`` method }}} -Well! to find the Euclidean norm and Infinity norm we have an even easier +Well! to find the Frobenius norm and Infinity norm we have an even easier method, and let us see that now. The norm of a matrix can be found out using the method -``norm()``. Inorder to find out the Euclidean norm of the matrix im5, +``norm()``. Inorder to find out the Frobenius norm of the matrix im5, we do, :: |