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Diffstat (limited to 'matrices/slides.org')
| -rw-r--r-- | matrices/slides.org | 27 |
1 files changed, 16 insertions, 11 deletions
diff --git a/matrices/slides.org b/matrices/slides.org index 34caa29..b7f56f2 100644 --- a/matrices/slides.org +++ b/matrices/slides.org @@ -42,11 +42,16 @@ * Creating a matrix - Creating a matrix using direct data - : In []: m1 = matrix([1, 2, 3, 4]) + : In []: m1 = array([1, 2, 3, 4]) - Creating a matrix using lists : In []: l1 = [[1,2,3,4],[5,6,7,8]] - : In []: m2 = matrix(l1) - - A matrix is basically an array + : In []: m2 = array(l1) +* Exercise 1 + Create a (2, 4) matrix ~m3~ + : m3 = [[5, 6, 7, 8], + : [9, 10, 11, 12]] +* Solution 1 + - m3 can be created as, : In []: m3 = array([[5,6,7,8],[9,10,11,12]]) * Matrix operations @@ -55,20 +60,20 @@ - Element-wise subtraction (both matrix should be of order ~mXn~) : In []: m3 - m2 * Matrix Multiplication - - Matrix Multiplication + - Element-wise multiplication using ~m3 * m2~ : In []: m3 * m2 + - Matrix Multiplication using ~dot(m3, m2)~ + : In []: dot(m3, m2) : Out []: ValueError: objects are not aligned - - Element-wise multiplication using ~multiply()~ - : multiply(m3, m2) * Matrix Multiplication (cont'd) - Create two compatible matrices of order ~nXm~ and ~mXr~ : In []: m1.shape - matrix m1 is of order ~1 X 4~ - Creating another matrix of order ~4 X 2~ - : In []: m4 = matrix([[1,2],[3,4],[5,6],[7,8]]) + : In []: m4 = array([[1,2],[3,4],[5,6],[7,8]]) - Matrix multiplication - : In []: m1 * m4 + : In []: dot(m1, m4) * Recall from ~array~ - The functions - ~identity(n)~ - @@ -86,11 +91,11 @@ * More matrix operations Transpose of a matrix : In []: m4.T -* Exercise 1 : Frobenius norm \& inverse +* Exercise 2 : Frobenius norm \& inverse Find out the Frobenius norm of inverse of a ~4 X 4~ matrix. : The matrix is - : m5 = matrix(arange(1,17).reshape(4,4)) + : m5 = arange(1,17).reshape(4,4) - Inverse of A, - #+begin_latex @@ -102,7 +107,7 @@ $||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}$ #+end_latex -* Exercise 2: Infinity norm +* Exercise 3 : Infinity norm Find the infinity norm of the matrix ~im5~ : - Infinity norm is defined as, |