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-* Matrices
-*** Outline
-***** Introduction
-******* Why do we want to do that?
-******* We shall use arrays (introduced before) for matrices
-******* Arsenal Required
-********* working knowledge of arrays
-***** Various matrix operations
-******* Transpose
-******* Sum of all elements
-******* Element wise operations
-******* Matrix multiplication
-******* Inverse of a matrix
-******* Determinant
-******* eigen values/vectors
-******* svd
-***** Other things available?
-*** Script
- Welcome.
-
- In this tutorial, you will learn how to perform some common matrix
- operations. We shall look at some of the functions available in
- pylab. Note that, this tutorial just scratches the surface and
- there is a lot more that can be done.
-
- Let's begin with finding the transpose of a matrix.
-
- In []: a = array([[ 1, 1, 2, -1],
- ...: [ 2, 5, -1, -9],
- ...: [ 2, 1, -1, 3],
- ...: [ 1, -3, 2, 7]])
-
- In []: a.T
-
- Type a, to observe the change in a.
- In []: a
-
- Now we shall look at adding another matrix b, to a. It doesn't
- require anything special, just use the + operator.
-
- In []: b = array([[3, 2, -1, 5],
- [2, -2, 4, 9],
- [-1, 0.5, -1, -7],
- [9, -5, 7, 3]])
- In []: a + b
-
- What do you expect would be the result, if we used * instead of
- the + operator?
-
- In []: a*b
-
- You get an element-wise product of the two arrays and not a matrix
- product. To get a matrix product, we use the dot function.
-
- In []: dot(a, b)
-
- The sum function returns the sum of all the elements of the
- array.
-
- In []: sum(a)
-
- The inv command returns the inverse of the matrix.
- In []: inv(a)
-
- In []: det(a)
-
- In []: eig(a)
- Returns the eigenvalues and the eigen vectors.
-
- In []: eigvals(a)
- Returns only the eigenvalues.
-
- In []: svd(a)
- Singular Value Decomposition
-
-*** Notes
-